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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


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


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


ASYMPTOTICALLY ISOCHRONOUS SYSTEMS

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/9780199535286.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In Chapter 6—reporting very recent findings (although the main idea is not new)—autonomous dynamical systems are treated whose generic solutions approach asymptotically (at large time) 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.


MODELS OF MANY-CHAIN SYSTEMS

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses methods for converting the many body problem in interacting polymer fluids to a statistical field theory. Auxiliary field transforms are introduced, that decouple interactions ... More


Applications of path integrals

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0014
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses some applications of path integrals. First, it illustrates how their qualitative use can yield insights. As an example, it applies it to the so-called Bohm–Aharonov effect. ... More


Introduction

Andrew Zangwill

in A Mind Over Matter: Philip Anderson and the Physics of the Very Many

Published in print:
2021
Published Online:
January 2021
ISBN:
9780198869108
eISBN:
9780191905599
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198869108.003.0001
Subject:
Physics, History of Physics

This chapter provides an overview of Anderson’s career and contrasts his speciality, the physics of the very many (solid-state physics), with the areas of physics that tend to appear in popular ... More


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