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.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-0326-4 (9780821803264)
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Schweitzer Klassifikation
The Hamiltonian double-zero eigenvalue by H. Broer, S.-N. Chow, Y. I. Kim, and G. Vegter Geometric analysis of the effect of symmetry breaking perturbations on an $O(2)$ invariant homoclinic cycle by P. Chossat and M. J. Field Bifurcation in a flow-induced vibration model by R. Corless Dynamics near an irrational collision of Eigenvalues for symplectic mappings by T. J. Bridges, R. H. Cushman, and R. S. Mackay The constrained Liapunov-Schmidt procedure and periodic orbits by M. Golubitsky, J. E. Marsden, I. Stewart, and M. Dellnitz Whiskered tori and chaos in resonant Hamiltonian normal forms by G. Haller and S. R. Wiggins Normal forms for perturbations of the Euler top by H. Hanssmann A homoclinic orbit of the Lorenz system by precise shooting by B. Hassard and J. Zhang Homoclinic intermittency by A. J. Homburg A codimension $2$ bifurcation for reversible vector fields by G. Iooss Nonasymptotically stable attractors in $O(2)$ mode interactions by M. Krupa and I. Melbourne Determining the global topology of resonance surfaces for periodically forced oscillator families by R. P. McGehee and B. B. Peckham Normal forms and homoclinic chaos: Application to structural systems by N. S. Namachchivaya and N. Malhotra A general reduction method for periodic solutions near equilibria in Hamiltonian systems by A. L. Vanderbauwhede and J.-C. Van Der Meer.
