**Fields Institute Communications**

Volume: 4;
1995;
294 pp;
Hardcover

MSC: Primary 58;

Print ISBN: 978-0-8218-0326-4

Product Code: FIC/4

List Price: $125.00

Individual Member Price: $100.00

**Electronic ISBN: 978-1-4704-2972-0
Product Code: FIC/4.E**

List Price: $125.00

Individual Member Price: $100.00

# Normal Forms and Homoclinic Chaos

Share this page *Edited by *
*William F. Langford; Wayne Nagata*

A co-publication of the AMS and Fields Institute

This volume presents new research on normal forms,
symmetry, homoclinic cycles, and chaos, from the Workshop on Normal
Forms and Homoclinic Chaos held during The Fields Institute Program Year
on Dynamical Systems and Bifurcation Theory in November 1992,
in Waterloo, Canada. The workshop bridged the local and global
analysis of dynamical systems with emphasis on normal forms and the
recently discovered homoclinic cycles which may arise in normal
forms.

Specific topics covered in this volume
include…

- normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps;
- the effects of symmetry on normal forms;
- the persistence of homoclinic cycles;
- symmetry-breaking, both spontaneous and induced;
- mode interactions;
- resonances;
- intermittency;
- numerical computation of orbits in phase space;
- applications to flow-induced vibrations and to mechanical and structural systems;
- general methods for calculation of normal forms;
- chaotic dynamics arising from normal forms.

Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Normal Forms and Homoclinic Chaos

- Cover Cover11
- Titles in series i2
- Title page v6
- Contents vii8
- Preface ix10
- The Hamiltonian double-zero eigenvalue 116
- Geometric analysis of the effect of symmetry breaking perturbations on an 𝑂(2) invariant homoclinic cycle 2136
- Bifurcation in a flow-induced vibration model 4358
- Dynamics near an irrational collision of Eigenvalues for symplectic mappings 6176
- The constrained Liapunov-Schmidt procedure and periodic orbits 8196
- Whiskered tori and chaos in resonant Hamiltonian normal forms 129144
- Normal forms for perturbations of the Euler top 151166
- A homoclinic orbit of the Lorenz system by precise shooting 175190
- Homoclinic intermittency 191206
- A codimension 2 bifurcation for reversible vector fields 201216
- Nonasymptotically stable attractors in 𝑂(2) mode interactions 219234
- Determining the global topology of resonance surfaces for periodically forced oscillator families 233248
- Normal forms and homoclinic chaos: Application to structural systems 253268
- A general reduction method for periodic solutions near equilibria in Hamiltonian systems 273288
- Back Cover Back Cover1311

#### Readership

Research mathematicians, physicists, other scientists, and engineers.