Anosov Diffeomorphisms on Nilmanifolds
نویسندگان
چکیده
منابع مشابه
Hyperbolic Automorphisms and Anosov Diffeomorphisms on Nilmanifolds
We translate the problem of finding Anosov diffeomorphisms on a nilmanifold which is covered by a free nilpotent Lie group into a problem of constructing matrices in GL(n,Z) whose eigenvalues satisfy certain conditions. Afterwards, we show how this translation can then be solved in some specific situations. The paper starts with a section on polynomial permutations of QK , a subject which is of...
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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 show by means of a counterexample that a C diffeomorphism Hölder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to C. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a C diffeomorphism Hölder conjugate to an Anosov diffeomorphism is Anosov itself provided that Hölder exponents of the conjugacy and its invers...
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We associate with each graph (S, E) a 2-step simply connected nilpotent Lie group N and a lattice Γ in N . We determine the group of Lie automorphisms of N and apply the result to describe a necessary and sufficient condition, in terms of the graph, for the compact nilmanifold N/Γ to admit an Anosov automorphism. Using the criterion we obtain new examples of compact nilmanifolds admitting Anoso...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2039303