Isochronous systems / Francesco Calogero.

Format:

Book

Author/Creator:

Calogero, Francesco.

Language:

English

Subjects (All):

Dynamics.

System analysis.

Differential equations.

Physical Description:

1 online resource (261 p.)

Place of Publication:

Oxford ; New York : Oxford University Press, 2008.

Language Note:

English

Summary:

A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large class of dynamical systems, that yields autonomous systems which are isochronous. This justifies the notion that isochronous systems are not rare.In this book the procedure to manufacture isochronous systems is reviewed, and many examples of such systems are provided. Examples include many-body problems characte

Contents:

Contents; 1 Introduction; 1.N Notes to Chapter 1; 2 Isochronous systems are not rare; 2.1 The trick; 2.2 Examples; 2.N Notes to Chapter 2; 3 A single ODE of arbitrary order; 3.1 A class of autonomous ODEs; 3.2 Examples; 3.2.1 First-order algebraic complex ODE; 3.2.2 Polynomial vector field in the plane; 3.2.3 Oscillator with additional inverse-cube force; 3.2.4 Isochronous versions of the first and second Painlevé ODEs (complex and real versions); 3.2.5 Autonomous second-order ODEs (complex and real versions); 3.2.6 Autonomous third-order ODEs (complex and real versions)

3.2.7 Isochronous version of a solvable second-order ODE due to Painlevé3.2.8 Isochronous versions of five solvable ODEs due to Chazy; 3.N Notes to Chapter 3; 4 Systems of ODEs: many-body problems, nonlinear harmonic oscillators; 4.1 A class of isochronous dynamical systems; 4.1.1 A lemma; 4.1.2 Examples; 4.2 One-dimensional systems; 4.2.1 Many-body problems with two-body velocity-independent forces; 4.2.2 Goldfishing; 4.2.3 Nonlinear oscillators; 4.2.4 Two Hamiltonian systems; 4.3 Two-dimensional systems; 4.4 Three-dimensional systems; 4.5 Multi-dimensional systems; 4.N Notes to Chapter 4

5 Isochronous Hamiltonian systems are not rare5.1 Another trick; 5.2 Partially isochronous Hamiltonian systems; 5.2.1 A simple variant; 5.2.2 A more general variant; 5.3 More general Hamiltonians; 5.4 Examples; 5.5 Yet another trick; 5.5.1 Main results; 5.5.2 Transient chaos; 5.5.3 A simple example; 5.5.4 Quantization: equispaced spectrum; 5.N Notes to Chapter 5; 6 Asymptotically isochronous systems; 6.1 An asymptotically isochronous class of solvable many-body problems; 6.1.1 A specific example; 6.2 A (generally nonintegrable) class of asymptotically isochronous many-body models

6.2.1 A theorem and its proof6.3 Some additional considerations; 7 Isochronous PDEs; 7.1 The trick for PDEs; 7.2 A list of isochronous PDEs; 7.3 PDEs with lots of solutions periodic in time and in space; 7.N Notes to Chapter 7; 8 Outlook; 8.N Notes to Chapter 8; A Some useful identities; B Two proofs; C Diophantine findings and conjectures; References; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; W; Y; Z

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references (p. [239]-247) and index.

ISBN:

0-19-965752-1

1-281-85322-4

9786611853228

0-19-153865-5

OCLC:

213487276