Non-stationary compositions of Anosov diffeomorphisms
نویسندگان
چکیده
منابع مشابه
Non-stationary Compositions of Anosov Diffeomorphisms
Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a 2-dimensional compact Riemannian manifold, which are allowed to change with time — slowly, but in a rather arbitrary fashion. In particular, such systems admit...
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Definition 1. Let < , > be a C∞ Riemannian metric on M and | · | its induced norm on TxM for each x ∈ M . We say that f ∈ D is Anosov if 1. the tangent bundle of M splits in a Whitney direct sum of continuous subbundles TM = E ⊕ E, where E and E are Df -invariant, 2. there exists constants c, c′ > 0 and 0 < λ < 1 such that |Dfn xv| < c λn|v| |Df−n x w| < c′ λn|w| for all x ∈ M , v ∈ E x, and w ...
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We consider the class of Rn extensions of Anosov diffeomorphisms on infranilmanifolds, and find necessary and sufficient conditions for topological transitivity. In particular, if the fiber is R, the existence of a semi-orbit with the projection on R unbounded from above and from below is equivalent to topological transitivity. We also show that in the above class topological transitivity and s...
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In 1969, Hirsch posed the following problem: given a diffeomorphism f : N → N , and a compact invariant hyperbolic set Λ of f , describe the topology of Λ and the dynamics of f restricted to Λ. We solve the problem where Λ = M is a closed 3-manifold: if M is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions....
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2011
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/24/10/016