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Multi-pulse evolution and space-time chaos in dissipative systems. (English) Zbl 1163.37003
Mem. Am. Math. Soc. 925, 97 p. (2009).
The authors study semilinear parabolic systems that admit a family of exponentially decaying pulse-like steady states obtained via transformations. The multi-pulse solutions are the sum of infinitely number of well separated pulses. The authors prove a global center-manifold reduction theorem for the temporal evolution of such solutions. They also verify the existence of Sinai-Bunimovich space-time chaos in the 1D space-time periodically forced Swift-Hohenberg equation.

MSC:
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
35Q30 Navier-Stokes equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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