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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
Available Formats:
Hardcover ISBN: 978-0-8218-0326-4
Product Code: FIC/4
List Price: $133.00 MAA Member Price:$119.70
AMS Member Price: $106.40 Electronic ISBN: 978-1-4704-2972-0 Product Code: FIC/4.E List Price:$125.00
MAA Member Price: $112.50 AMS Member Price:$100.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $199.50 MAA Member Price:$179.55
AMS Member Price: $159.60 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 Available Formats:  Hardcover ISBN: 978-0-8218-0326-4 Product Code: FIC/4  List Price:$133.00 MAA Member Price: $119.70 AMS Member Price:$106.40
 Electronic ISBN: 978-1-4704-2972-0 Product Code: FIC/4.E
 List Price: $125.00 MAA Member Price:$112.50 AMS Member Price: $100.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$199.50 MAA Member Price: $179.55 AMS Member Price:$159.60
• 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.

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
• Request Review Copy
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.

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
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