# Hamiltonian Dynamical Systems

DOI link for Hamiltonian Dynamical Systems

Hamiltonian Dynamical Systems book

# Hamiltonian Dynamical Systems

DOI link for Hamiltonian Dynamical Systems

Hamiltonian Dynamical Systems book

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Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

## TABLE OF CONTENTS

part Part 1|73 pages

Introductory Articles

chapter |7 pages

#### Is the Solar System Stable?

part Part 2|162 pages

Equilibria and Periodic Orbits

chapter |3 pages

#### Linear Stability of Periodic Orbits in Lagrangian Systems

chapter |19 pages

#### Universal Behaviour in Families of Area-Preserving Maps

chapter |27 pages

#### Quasi-Elliptic Periodic Points in Conservative Dynamical Systems.

part Part 3|167 pages

Quasiperiodic Orbits

chapter |21 pages

#### Geodesics on a Two-Dimensional Riemannian Manifold with Periodic Coefficients. 1

chapter |107 pages

#### Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics

part Part 4|75 pages

Breakup of Invariant Tori

chapter |4 pages

#### Destruction of Magnetic Surfaces by Magnetic Field Irregularities

chapter |18 pages

#### A Renormalisation Approach to Invariant Circles in Area-Preserving Maps

part Part 5|85 pages

Chaotic Behaviour

chapter |3 pages

#### Roughness of Geodesic Flows on Compact Riemannian Manifolds of Negative Curvature

chapter |4 pages

#### Ergodic Properties of Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature

chapter |4 pages

#### Ljapunov Characteristic Exponents and Ergodic Properties of Smooth Dynamical Systems with an Invariant Measure

chapter |24 pages

#### Principles for the Design of Billiards with Nonvanishing Lyapunov Exponents

part Part 6|86 pages

Mixed Systems

chapter |12 pages

#### A Model Problem with the Coexistence of Stochastic and Integrable Behaviour

chapter |7 pages

#### Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems a)

chapter |6 pages

#### Arnold Diffusion, Ergodicity and Intermittency in a Coupled Standard Mapping

part Part 7|112 pages

Applications