Chaotic Billiards

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Chaotic Billiards

Author : Nikolai Chernov
Publisher : American Mathematical Society
ISBN 13 : 1470474425
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Chaotic Billiards by : Nikolai Chernov

Download or read book Chaotic Billiards written by Nikolai Chernov and published by American Mathematical Society. This book was released on 2023-09-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

Chaotic Billiards

Author : Nikolai Chernov
Publisher : American Mathematical Soc.
ISBN 13 : 0821840967
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Chaotic Billiards by : Nikolai Chernov

Download or read book Chaotic Billiards written by Nikolai Chernov and published by American Mathematical Soc.. This book was released on 2006 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so faronly book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefullydesigned exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

Geometry and Billiards

Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821839195
Total Pages : 192 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry and Billiards by : Serge Tabachnikov

Download or read book Geometry and Billiards written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.

An Introduction To Mathematical Billiards

Author : Utkir A Rozikov
Publisher : World Scientific
ISBN 13 : 9813276487
Total Pages : 223 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis An Introduction To Mathematical Billiards by : Utkir A Rozikov

Download or read book An Introduction To Mathematical Billiards written by Utkir A Rozikov and published by World Scientific. This book was released on 2018-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This book offers one of the few places where a collection of results from the literature can be found … The book has an extensive bibliography … It is very nice to have the compendium of results that is presented here.'zbMATHA mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.

Chaos Theory: Bullet Guides

Author : Ron Poet
Publisher : John Murray
ISBN 13 : 1444144413
Total Pages : 89 pages
Book Rating : 4.4/5 (441 download)

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Book Synopsis Chaos Theory: Bullet Guides by : Ron Poet

Download or read book Chaos Theory: Bullet Guides written by Ron Poet and published by John Murray. This book was released on 2011-11-25 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Open this book and you will Discover the origins of chaos theory Investigate complex systems Understand the causes of chaos Become aware of its everyday implications

Directions In Chaos - Volume 2

Author : Bailin Hao
Publisher : World Scientific
ISBN 13 : 9814513725
Total Pages : 400 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Directions In Chaos - Volume 2 by : Bailin Hao

Download or read book Directions In Chaos - Volume 2 written by Bailin Hao and published by World Scientific. This book was released on 1988-04-01 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.

Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

Author : Rainer Klages
Publisher : World Scientific
ISBN 13 : 9812771514
Total Pages : 458 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics by : Rainer Klages

Download or read book Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics written by Rainer Klages and published by World Scientific. This book was released on 2007 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory. Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity. Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors. The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Author : Elbert E. N. Macau
Publisher : Springer
ISBN 13 : 3319785125
Total Pages : 232 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems by : Elbert E. N. Macau

Download or read book A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems written by Elbert E. N. Macau and published by Springer. This book was released on 2018-06-14 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Quantum Chaos and Quantum Dots

Author : Katsuhiro Nakamura
Publisher :
ISBN 13 : 9780198525899
Total Pages : 228 pages
Book Rating : 4.5/5 (258 download)

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Book Synopsis Quantum Chaos and Quantum Dots by : Katsuhiro Nakamura

Download or read book Quantum Chaos and Quantum Dots written by Katsuhiro Nakamura and published by . This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. Billiards can nowadays be created as quantum dots in the microscopic world enabling one to envisage the so-called quantum chaos, i.e.quantum manifestation of chaos of billiard balls. In fact, owing to recent progress in advanced technology, nanoscale quantum dots, such as chaotic stadium and antidot lattices analogous to the Sinai Billiard, can be fabricated at the interface of semiconductor heterojunctions. This book begins itsexploration of the effect of chaotic electron dynamics on ballistic quantum transport in quantum dots with a puzzling experiment on resistance fluctuations for stadium and circle dots. Throughout the text, major attention is paid to the semiclassical theory which makes it possible to interpretquantum phenomena in the language of the classical world. Chapters one to four are concerned with the elementary statistical methods (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and escape rate), which are needed for a semiclassical description of transport in quantum dots. Chapters fiveto ten discuss the topical subjects in the field, including the ballistic weak localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, persistent current, Arnold diffusion and Coulomb blockade.

Computational Statistical Physics

Author : K.-H. Hoffmann
Publisher : Springer Science & Business Media
ISBN 13 : 9783540421603
Total Pages : 330 pages
Book Rating : 4.4/5 (216 download)

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Book Synopsis Computational Statistical Physics by : K.-H. Hoffmann

Download or read book Computational Statistical Physics written by K.-H. Hoffmann and published by Springer Science & Business Media. This book was released on 2002 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

Mathematical Modeling, Simulation, Visualization and e-Learning

Author : Dialla Konaté
Publisher : Springer Science & Business Media
ISBN 13 : 3540743391
Total Pages : 365 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Mathematical Modeling, Simulation, Visualization and e-Learning by : Dialla Konaté

Download or read book Mathematical Modeling, Simulation, Visualization and e-Learning written by Dialla Konaté and published by Springer Science & Business Media. This book was released on 2007-12-08 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features articles written by some of the most prominent leading applied mathematicians as well as young and promising ones. The common objective of these articles is to present an important issue which is currently widely discussed in scientific investigation with major human, economic or ecological implications. Each article is as deep as an expert lecture but is also self-contained, so that even isolated scientists with limited resources can profit greatly from it.

Chaos

Author : Hans Jürgen Korsch
Publisher : Springer Science & Business Media
ISBN 13 : 3662038668
Total Pages : 327 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Chaos by : Hans Jürgen Korsch

Download or read book Chaos written by Hans Jürgen Korsch and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible.

The Transition to Chaos

Author : Linda Reichl
Publisher : Springer Science & Business Media
ISBN 13 : 1475743505
Total Pages : 692 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Transition to Chaos by : Linda Reichl

Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.

Directions in Chaos

Author : Bai-lin Hao
Publisher : World Scientific
ISBN 13 : 9789971503628
Total Pages : 402 pages
Book Rating : 4.5/5 (36 download)

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Book Synopsis Directions in Chaos by : Bai-lin Hao

Download or read book Directions in Chaos written by Bai-lin Hao and published by World Scientific. This book was released on 1987 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.

Encyclopedia of Nonlinear Science

Author : Alwyn Scott
Publisher : Routledge
ISBN 13 : 1135455570
Total Pages : 2881 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Encyclopedia of Nonlinear Science by : Alwyn Scott

Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 2881 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Emerging Applications of Number Theory

Author : Dennis A. Hejhal
Publisher : Springer Science & Business Media
ISBN 13 : 9780387988245
Total Pages : 716 pages
Book Rating : 4.9/5 (882 download)

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Book Synopsis Emerging Applications of Number Theory by : Dennis A. Hejhal

Download or read book Emerging Applications of Number Theory written by Dennis A. Hejhal and published by Springer Science & Business Media. This book was released on 1999-05-21 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Irregular Atomic Systems and Quantum Chaos

Author : Jean-Claude Gay
Publisher : CRC Press
ISBN 13 : 9782881244827
Total Pages : 386 pages
Book Rating : 4.2/5 (448 download)

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Book Synopsis Irregular Atomic Systems and Quantum Chaos by : Jean-Claude Gay

Download or read book Irregular Atomic Systems and Quantum Chaos written by Jean-Claude Gay and published by CRC Press. This book was released on 1992 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the study of irregular behavior in few-body systems, with emphasis on the aspects of atomic physics. Areas covered include the atom in a magnetic field, microwave ionization of Rydberg atoms, and quasi-Wigner crystals in ion traps. All but one of the papers first appeared in volume 25 of the journal Comments on atomic and molecular physics. No index. Annotation copyrighted by Book News, Inc., Portland, OR