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ISOCHRONOUS HAMILTONIAN SYSTEMS ARE NOT RARE

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 5 various tricks are introduced, transforming Hamiltonian systems into isochronous Hamiltonian systems. The possibility to apply this procedure to large classes of Hamiltonian systems ... More


Hamiltonian Systems

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

When a system involves no dissipative mechanisms such as friction, we say that the system is conservative because its total energy is conserved and the behaviour is described by a time-independent ... More


Isochronous Systems

Francesco Calogero

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ... More


SYSTEMS OF ODEs: MANY-BODY PROBLEMS, NONLINEAR HARMONIC OSCILLATORS

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 4—the longer one in this book—a lemma is first introduced and several isochronous systems of ODEs encompassed by it are treated. One-, two-, three- and multi-dimensional isochronous ... More


INTRODUCTION

Francesco Calogero

in Isochronous Systems

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the introductory Chapter 1 a few representative instances of isochronous dynamical systems are tersely reviewed.


Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Vadim Kaloshin and Ke Zhang

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was ... More


Introduction

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter provides an overview of Arnold diffusion. The famous question called the ergodic hypothesis, formulated by Maxwell and Boltzmann, suggests that for a typical Hamiltonian on ... More


Forcing equivalence between kissing cylinders

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter formulates and proves the jump mechanism. It constructs a variational problem which proves forcing equivalence for the original Hamiltonian using Definition 6.18. It first constructs a ... More


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