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Normal Forms and Homoclinic Chaos
Edited by: William F. Langford, University of Guelph, ON, Canada, and Wayne Nagata, University of British Columbia, Vancouver, BC, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
1995; 294 pp; hardcover
Volume: 4
ISBN-10: 0-8218-0326-3
ISBN-13: 978-0-8218-0326-4
List Price: US$119
Member Price: US$95.20
Order Code: FIC/4
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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).

Readership

Research mathematicians, physicists, other scientists, and engineers.

Table of Contents

  • H. Broer, S.-N. Chow, Y. I. Kim, and G. Vegter -- The Hamiltonian double-zero eigenvalue
  • P. Chossat and M. J. Field -- Geometric analysis of the effect of symmetry breaking perturbations on an \(O(2)\) invariant homoclinic cycle
  • R. Corless -- Bifurcation in a flow-induced vibration model
  • T. J. Bridges, R. H. Cushman, and R. S. Mackay -- Dynamics near an irrational collision of Eigenvalues for symplectic mappings
  • M. Golubitsky, J. E. Marsden, I. Stewart, and M. Dellnitz -- The constrained Liapunov-Schmidt procedure and periodic orbits
  • G. Haller and S. R. Wiggins -- Whiskered tori and chaos in resonant Hamiltonian normal forms
  • H. Hanßmann -- Normal forms for perturbations of the Euler top
  • B. Hassard and J. Zhang -- A homoclinic orbit of the Lorenz system by precise shooting
  • A. J. Homburg -- Homoclinic intermittency
  • G. Iooss -- A codimension \(2\) bifurcation for reversible vector fields
  • M. Krupa and I. Melbourne -- Nonasymptotically stable attractors in \(O(2)\) mode interactions
  • R. P. McGehee and B. B. Peckham -- Determining the global topology of resonance surfaces for periodically forced oscillator families
  • N. S. Namachchivaya and N. Malhotra -- Normal forms and homoclinic chaos: Application to structural systems
  • A. L. Vanderbauwhede and J.-C. Van Der Meer -- A general reduction method for periodic solutions near equilibria in Hamiltonian systems
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