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Symplectic Twist Maps Global Variational Techniques
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Book Synopsis Symplectic Twist Maps by : Christophe Golé
Download or read book Symplectic Twist Maps written by Christophe Golé and published by World Scientific. This book was released on 2001 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 0. Introduction. 1. Fall from paradise. 2. Billiards and broken geodesies. 3. An ancestor of symplectic topology -- 1. Twist maps of the annulus. 4. Monotone twist maps of the annulus. 5. Generating functions and variational setting. 6. Examples. 7. The Poincare-Birkhoff theorem -- 2. The Aubry-Mather theorem. 8. Introduction. 9. Cyclically ordered sequences and orbits. 10. Minimizing orbits. 11. CO orbits of all rotation numbers. 12. Aubry-Mather sets -- 3. Ghost circles. 14. Gradient flow of the action. 15. The gradient flow and the Aubry-Mather theorem. 16. Ghost circles. 17. Construction of ghost circles. 18. Construction of disjoint ghost circles. 19. Proof of lemma 18.5. 20. Proof of theorem 18.1. 21. Remarks and applications. 22. Proofs of monotonicity and of the Sturmian lemma -- 4. Symplectic twist maps. 23. Symplectic twist maps of T[symbol] x IR[symbol]. 24. Examples. 25. More on generating functions. 2.6. Symplectic twist maps on general cotangent bundles of compact manifolds -- 5. Periodic orbits for symplectic twist maps of T[symbol] x IR[symbol]. 27. Presentation of the results. 28. Finite dimensional variational setting. 29. Second variation and nondegenerate periodic orbits. 30. The coercive case. 31. Asymptotically linear systems. 32. Ghost tori. 33. Hyperbolicity Vs. action minimizers -- 6. Invariant manifolds. 34. The theory of Kolmogorov-Arnold-Moser. 35. Properties of invariant tori. 36. (Un)stable manifolds and heteroclinic orbits. 37. Instability, transport and diffusion -- 7. Hamiltonian systems vs. twist maps. 38. Case study: The geodesic flow. 39. Decomposition of Hamiltonian maps into twist maps. 40. Return maps in Hamiltonian systems. 41. Suspension of symplectic twist maps by Hamiltonian flows -- 8. Periodic orbits for Hamiltonian systems. 42. Periodic orbits in the cotangent of the n-torus. 43. Periodic orbits in general cotangent spaces. 44. Linking of spheres -- 9. Generalizations of the Aubry-Mather theorem. 45. Theory for functions on lattices and PDE's. 46. Monotone recurrence relationst. 47. Anti-integrable limit. 48. Mather's theory of minimal measures. 49. The case of hyperbolic manifolds. 50. Concluding remarks -- 10. Generating phases and symplectic topology. 51. Chaperon's method and the theorem Of Conley-Zehnder. 52. Generating phases and symplectic geometry.
Book Synopsis Symplectic Twist Maps: Global Variational Techniques by : Christophe Gole
Download or read book Symplectic Twist Maps: Global Variational Techniques written by Christophe Gole and published by World Scientific. This book was released on 2001-11-22 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.
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 1107 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.
Download or read book Ergodic Theory written by Idris Assani and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-06-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable
Book Synopsis Elementary Symplectic Topology and Mechanics by : Franco Cardin
Download or read book Elementary Symplectic Topology and Mechanics written by Franco Cardin and published by Springer. This book was released on 2014-12-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.
Book Synopsis Playing Around Resonance by : Alessandro Fonda
Download or read book Playing Around Resonance written by Alessandro Fonda and published by Birkhäuser. This book was released on 2016-11-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.
Book Synopsis Revista Matemática Iberoamericana by :
Download or read book Revista Matemática Iberoamericana written by and published by . This book was released on 2016 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Digital Signal Processing with Matlab Examples, Volume 1 by : Jose Maria Giron-Sierra
Download or read book Digital Signal Processing with Matlab Examples, Volume 1 written by Jose Maria Giron-Sierra and published by Springer. This book was released on 2016-11-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs. This book includes MATLAB codes to illustrate each of the main steps of the theory, offering a self-contained guide suitable for independent study. The code is embedded in the text, helping readers to put into practice the ideas and methods discussed. The book is divided into three parts, the first of which introduces readers to periodic and non-periodic signals. The second part is devoted to filtering, which is an important and commonly used application. The third part addresses more advanced topics, including the analysis of real-world non-stationary signals and data, e.g. structural fatigue, earthquakes, electro-encephalograms, birdsong, etc. The book’s last chapter focuses on modulation, an example of the intentional use of non-stationary signals.
Download or read book Nonlinearity written by and published by . This book was released on 2005 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Book Synopsis Discrete and Continuous Dynamical Systems by :
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2006 with total page 894 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The British National Bibliography by : Arthur James Wells
Download or read book The British National Bibliography written by Arthur James Wells and published by . This book was released on 2002 with total page 1896 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl
Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Hamiltonian Reduction by Stages by : Jerrold E. Marsden
Download or read book Hamiltonian Reduction by Stages written by Jerrold E. Marsden and published by Springer. This book was released on 2007-06-05 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Book Synopsis Impact of a Pseudo-rigid Ball on a Rigid Foundation by : Eva Adnan Kanso
Download or read book Impact of a Pseudo-rigid Ball on a Rigid Foundation written by Eva Adnan Kanso and published by . This book was released on 2003 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Billiards written by Serge Tabachnikov and published by SMF. This book was released on 1995 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
