On Iterations Of Misiurewiczs Rational Maps On The Riemann Sphere

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Iteration of Rational Functions

Author : Alan F. Beardon
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951515
Total Pages : 308 pages
Book Rating : 4.9/5 (515 download)

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Book Synopsis Iteration of Rational Functions by : Alan F. Beardon

Download or read book Iteration of Rational Functions written by Alan F. Beardon and published by Springer Science & Business Media. This book was released on 2000-09-27 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.

Analytic Endomorphisms of the Riemann Sphere

Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110769891
Total Pages : 487 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Analytic Endomorphisms of the Riemann Sphere by : Mariusz Urbański

Download or read book Analytic Endomorphisms of the Riemann Sphere written by Mariusz Urbański and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on thermodynamic, ergodic and fractal properties of these functions (notably, equilibrium states, Bowen's formula and Sullivan’s conformal measures). This volume builds on the first two volumes in the series while simultaneously developing some methods and techniques specific to rational functions.

Thermodynamic Formalism

Author : Mark Pollicott
Publisher : Springer Nature
ISBN 13 : 3030748634
Total Pages : 536 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Thermodynamic Formalism by : Mark Pollicott

Download or read book Thermodynamic Formalism written by Mark Pollicott and published by Springer Nature. This book was released on 2021-10-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.

Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets

Author : Robert L. Devaney
Publisher : American Mathematical Soc.
ISBN 13 : 0821802909
Total Pages : 223 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets by : Robert L. Devaney

Download or read book Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets written by Robert L. Devaney and published by American Mathematical Soc.. This book was released on 1994 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.

International Conference On Dynamical Systems

Author : F Ledrappier
Publisher : CRC Press
ISBN 13 : 9780582302969
Total Pages : 260 pages
Book Rating : 4.3/5 (29 download)

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Book Synopsis International Conference On Dynamical Systems by : F Ledrappier

Download or read book International Conference On Dynamical Systems written by F Ledrappier and published by CRC Press. This book was released on 1997-05-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume clearly reflects Ricardo Mane's legacy, his contribution to mathematics and the diversity of his mathematical intersts. It contains fifteen refereed research papers on thems including Hamiltonian and Lagrangian dynamics, growth rate of the number of geodesics on a compact manifold, one dimensional complex and real dynamics, and bifurcations and singular cycles. This book also contains two famous sets of notes by Ricardo Mane. One is the seminal paper on Lagrangian dynamics that he had prepared for the conference; the other is on the genericity of zero exponents area preserving diffeomorphisms on surfaces when non Anosov. This book will be of particular interest to researchers and graduate students in mathematics, mechanics and mathematical physics.

Expanding Thurston Maps

Author : Mario Bonk
Publisher : American Mathematical Soc.
ISBN 13 : 082187554X
Total Pages : 497 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Expanding Thurston Maps by : Mario Bonk

Download or read book Expanding Thurston Maps written by Mario Bonk and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration. It is called expanding if, roughly speaking, preimages of a fine open cover of the underlying sphere under iterates of the map become finer and finer as the order of the iterate increases. Every expanding Thurston map gives rise to a fractal space, called its visual sphere. Many dynamical properties of the map are encoded in the geometry of this visual sphere. For example, an expanding Thurston map is topologically conjugate to a rational map if and only if its visual sphere is quasisymmetrically equivalent to the Riemann sphere. This relation between dynamics and fractal geometry is the main focus for the investigations in this work. The book is an introduction to the subject. The prerequisites for the reader are modest and include some basic knowledge of complex analysis and topology. The book has an extensive appendix, where background material is reviewed such as orbifolds and branched covering maps.

Ergodic Dynamics

Author : Jane Hawkins
Publisher : Springer Nature
ISBN 13 : 3030592421
Total Pages : 340 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Ergodic Dynamics by : Jane Hawkins

Download or read book Ergodic Dynamics written by Jane Hawkins and published by Springer Nature. This book was released on 2021-01-28 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.

Rational Maps of the Riemann Sphere

Author : Angelyn Jewell
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (34 download)

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Book Synopsis Rational Maps of the Riemann Sphere by : Angelyn Jewell

Download or read book Rational Maps of the Riemann Sphere written by Angelyn Jewell and published by . This book was released on 1979 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Israel Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 792 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Israel Journal of Mathematics by :

Download or read book Israel Journal of Mathematics written by and published by . This book was released on 1963 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Pressure for Multimodal Maps of the Interval

Author : Feliks Przytycki
Publisher : American Mathematical Soc.
ISBN 13 : 1470435675
Total Pages : 94 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric Pressure for Multimodal Maps of the Interval by : Feliks Przytycki

Download or read book Geometric Pressure for Multimodal Maps of the Interval written by Feliks Przytycki and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. The authors work in a setting of generalized multimodal maps, that is, smooth maps f of a finite union of compact intervals Iˆ in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. They prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pull-backs). They prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential −tlog|f′|, give the same value (including pressure on periodic orbits, “tree” pressure, variational pressures and conformal pressure). Finally they prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the “condensation” and “freezing” parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties.

Bulletin of the American Mathematical Society

Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 850 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society

Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2003 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 868 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Annales Academiae Scientiarum Fennicae

Author :
Publisher :
ISBN 13 :
Total Pages : 546 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Annales Academiae Scientiarum Fennicae by :

Download or read book Annales Academiae Scientiarum Fennicae written by and published by . This book was released on 1996 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applicationes Mathematicae

Author :
Publisher :
ISBN 13 :
Total Pages : 534 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Applicationes Mathematicae by :

Download or read book Applicationes Mathematicae written by and published by . This book was released on 2000 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Pluripotential Theory

Author : Giorgio Patrizio
Publisher : Springer
ISBN 13 : 3642364217
Total Pages : 328 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Pluripotential Theory by : Giorgio Patrizio

Download or read book Pluripotential Theory written by Giorgio Patrizio and published by Springer. This book was released on 2013-05-16 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.

Newton’s Method and Dynamical Systems

Author : H.-O. Peitgen
Publisher : Springer Science & Business Media
ISBN 13 : 9400922817
Total Pages : 227 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Newton’s Method and Dynamical Systems by : H.-O. Peitgen

Download or read book Newton’s Method and Dynamical Systems written by H.-O. Peitgen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory and Related Topics III

Author : Ulrich Krengel
Publisher : Springer
ISBN 13 : 354047076X
Total Pages : 243 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Ergodic Theory and Related Topics III by : Ulrich Krengel

Download or read book Ergodic Theory and Related Topics III written by Ulrich Krengel and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.