Dynamics, Bifurcation and Symmetry

Dynamics, Bifurcation and Symmetry : New Trends and New Tools

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This text contains a collection of 28 contributions on the topics of bifurcation theory and dynamical systems, mostly from the point of view of symmetry breaking, which has been revealed to be a powerful tool in the understanding of pattern formation and in the scientific application of these theories. Computational aspects of these theories are also considered. It is designed for graduate and postgraduate students of nonlinear applied mathematics, as well as any scientist or engineer interested in pattern formation and nonlinear instabilities. Dynamical systems and bifurcation theory are mathematical tools which are suitable for the study of time evolution and changes in the physical world. The introduction of the concept of symmetry and symmetry breaking in the theories enlarges their spectrum of application and their predictive capability in the evolution of physical systems.
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Product details

  • Hardback | 372 pages
  • 162.6 x 243.8 x 25.4mm | 771.12g
  • Dordrecht, Netherlands, United States
  • English
  • 29 SW-Abb., XV, 354 p.
  • 0792329589
  • 9780792329589

Table of contents

A spatial centre manifold approach to a hydrodynamical problem with O(2) symmetry; A. Afendikov, A. Mielke. Analyzing bifurcations in the Kolmogorov flow equations; D. Armbruster, P. Chossat, B. Nicolaenko, N. Smaoui. Oscillator networks with the symmetry of the unit quaternion group; P. Ashwin, G. Danglemayr, I. Stewart, M. Wegelin. An investigation of a mode interaction involving period-doubling and symmetry-breaking bifurcations; P.J. Aston. Sets, lines and adding machines; J. Buescu, I. Stewart. Mixed-mode solutions in mode interaction problems with symmetry; S. Castro. A classification of 2-modes interactions with SO(3) symmetry and applications; P. Chossat, F. Guyard. Nonlinear parabolic evolutions in unbounded domains; P. Collet. Eigenvalue movement for a class of reversible Hamiltonian systems with three degrees of freedom; M. Dellnitz, J. Scheurle. Blowing-up in equivariant bifurcation theory; M. Field. A remark on the detection of symmetry of attractors; K. Gatermann. Coupled cells: wreath products and direct products; M. Golubitsky, I. Stewart, B. Dionne. Hopf bifurcations on generalized rectangles with Neumann boundary conditions; G. Gomes, I. Stewart. The role of geometry in computational dynamics; J. Guckenheimer. Hopf bifurcation at k-fold resonances in equivariant reversible systems; J. Knobloch, A. Vanderbauwhede. Symmetries and reversing symmetries in kicked systems; J.S.W. Lamb, H. Brands. Exclusion of relative equilibria; R. Lauterbach, P. Chossat. Bifurcation of periodic orbits in 1:2 resonance: a singularity theory approach; V.G. LeBlanc, W.F. Langford. Hamiltonian structure of the reversible non-semisimple 1:1 resonance; J.C. van der Meer, J.A. Sanders, A. Vanderbauwhede. Instantaneous symmetry and symmetry on average in the Couette-Taylor and Faraday experiments; I. Melbourne. The path formulation of bifurcation theory; J. Montaldi. Co-dimension of two local analyses of spherical Benard convection; J.D. Rodriguez, C. Geiger, G. Danglemayr. A geometric Hamiltonian approach to the affine rigid body; E. Sousa Dias. A note on the discontinuous vector fields and reversible mappings; M.A. Teixeira. Bifurcation of singularities near reversible systems; M.A. Teixeira, A. Jacquemard. On a new phenomenon in bifurcations of periodic orbits; H. True. An inhomogeneous Picard-Fuchs equation; S.A. van Gils. Hopf bifurcation in symmetrically-coupled lasers; M. Wegelin.
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