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Normal Forms and Homoclinic Chaos
 
Edited by: William F. Langford University of Guelph, Guelph, ON, Canada
Wayne Nagata University of British Columbia, Vancouver, BC, Canada
A co-publication of the AMS and Fields Institute
Normal Forms and Homoclinic Chaos
Hardcover ISBN:  978-0-8218-0326-4
Product Code:  FIC/4
List Price: $140.00
MAA Member Price: $126.00
AMS Member Price: $112.00
eBook ISBN:  978-1-4704-2972-0
Product Code:  FIC/4.E
List Price: $132.00
MAA Member Price: $118.80
AMS Member Price: $105.60
Hardcover ISBN:  978-0-8218-0326-4
eBook: ISBN:  978-1-4704-2972-0
Product Code:  FIC/4.B
List Price: $272.00 $206.00
MAA Member Price: $244.80 $185.40
AMS Member Price: $217.60 $164.80
Normal Forms and Homoclinic Chaos
Click above image for expanded view
Normal Forms and Homoclinic Chaos
Edited by: William F. Langford University of Guelph, Guelph, ON, Canada
Wayne Nagata University of British Columbia, Vancouver, BC, Canada
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-0326-4
Product Code:  FIC/4
List Price: $140.00
MAA Member Price: $126.00
AMS Member Price: $112.00
eBook ISBN:  978-1-4704-2972-0
Product Code:  FIC/4.E
List Price: $132.00
MAA Member Price: $118.80
AMS Member Price: $105.60
Hardcover ISBN:  978-0-8218-0326-4
eBook ISBN:  978-1-4704-2972-0
Product Code:  FIC/4.B
List Price: $272.00 $206.00
MAA Member Price: $244.80 $185.40
AMS Member Price: $217.60 $164.80
  • Book Details
     
     
    Fields Institute Communications
    Volume: 41995; 294 pp
    MSC: Primary 58

    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
     
     
    • Chapters
    • H. Broer, Shui-Nee Chow, Yong Kim and G. Vegter — The Hamiltonian double-zero eigenvalue
    • Pascal Chossat and Michael Field — Geometric analysis of the effect of symmetry breaking perturbations on an $O(2)$ invariant homoclinic cycle
    • Robert Corless — Bifurcation in a flow-induced vibration model
    • Thomas Bridges, Richard Cushman and Robert Mackay — Dynamics near an irrational collision of Eigenvalues for symplectic mappings
    • Martin Golubitsky, Jerrold Marsden, Ian Stewart and Michael Dellnitz — The constrained Liapunov-Schmidt procedure and periodic orbits
    • Gyorgy Haller and Stephen Wiggins — Whiskered tori and chaos in resonant Hamiltonian normal forms
    • Heinz Hanßmann — Normal forms for perturbations of the Euler top
    • Brian Hassard and Jianhe Zhang — A homoclinic orbit of the Lorenz system by precise shooting
    • Ale Homburg — Homoclinic intermittency
    • Gerard Iooss — A codimension $2$ bifurcation for reversible vector fields
    • Martin Krupa and Ian Melbourne — Nonasymptotically stable attractors in $O(2)$ mode interactions
    • Richard McGehee and Bruce Peckham — Determining the global topology of resonance surfaces for periodically forced oscillator families
    • N. Namachchivaya and Naresh Malhotra — Normal forms and homoclinic chaos: Application to structural systems
    • A Vanderbauwhede and Jan-Cees Van Der Meer — A general reduction method for periodic solutions near equilibria in Hamiltonian systems
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 41995; 294 pp
MSC: Primary 58

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.

  • Chapters
  • H. Broer, Shui-Nee Chow, Yong Kim and G. Vegter — The Hamiltonian double-zero eigenvalue
  • Pascal Chossat and Michael Field — Geometric analysis of the effect of symmetry breaking perturbations on an $O(2)$ invariant homoclinic cycle
  • Robert Corless — Bifurcation in a flow-induced vibration model
  • Thomas Bridges, Richard Cushman and Robert Mackay — Dynamics near an irrational collision of Eigenvalues for symplectic mappings
  • Martin Golubitsky, Jerrold Marsden, Ian Stewart and Michael Dellnitz — The constrained Liapunov-Schmidt procedure and periodic orbits
  • Gyorgy Haller and Stephen Wiggins — Whiskered tori and chaos in resonant Hamiltonian normal forms
  • Heinz Hanßmann — Normal forms for perturbations of the Euler top
  • Brian Hassard and Jianhe Zhang — A homoclinic orbit of the Lorenz system by precise shooting
  • Ale Homburg — Homoclinic intermittency
  • Gerard Iooss — A codimension $2$ bifurcation for reversible vector fields
  • Martin Krupa and Ian Melbourne — Nonasymptotically stable attractors in $O(2)$ mode interactions
  • Richard McGehee and Bruce Peckham — Determining the global topology of resonance surfaces for periodically forced oscillator families
  • N. Namachchivaya and Naresh Malhotra — Normal forms and homoclinic chaos: Application to structural systems
  • A Vanderbauwhede and Jan-Cees Van Der Meer — A general reduction method for periodic solutions near equilibria in Hamiltonian systems
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.