Multi Pulse Evolution And Space Time Chaos In Dissipative Systems
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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems
Author: Sergey Zelik
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-03-06
The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.
The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations
Author: Tobias H. Jger
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-08-07
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture
Author: Luchezar N. Stoyanov
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.