Strange attractors for periodically forced parabolic equations / Kening Lu, Qiudong Wang, Lai-Sang Young

Auteur principal : Lu, Kening, 1962-, AuteurCo-auteur : Young, Lai-Sang, 1952-, Auteur • Wang, Qiudong, 1962-, AuteurType de document : MonographieCollection : Memoirs of the American Mathematical Society, 1054Langue : anglais.Pays: Etats Unis.Éditeur : Providence (R.I.) : American Mathematical Society, 2013, cop. 2012Description : 1 vol. (V-85 p.) : fig. ; 26 cmISBN: 9780821884843.ISSN: 0065-9266.Bibliographie : Bibliogr. p. 83-85.Sujet MSC : 37L30, Infinite-dimensional dissipative dynamical systems, Attractors and their dimensions, Lyapunov exponents
37D45, Dynamical systems with hyperbolic behavior, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G15, Local and nonlocal bifurcation theory for dynamical systems, Bifurcations of limit cycles and periodic orbits in dynamical systems
35B41, Qualitative properties of solutions to partial differential equations, AttractorsEn-ligne : Site de l'auteur
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Bibliogr. p. 83-85

We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

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