منابع مشابه
Anosov automorphisms on certain classes of nilmanifolds
We give a necessary and sufficient condition for k-step nilmanifolds associated with graphs (k ≥ 3) to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step nilmanifolds. 2000 Mathematics Subject Classification. Primary 37D20; Secondary 22E25
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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...
متن کاملAnosov Automorphisms on Compact Nilmanifolds Associated with Graphs
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...
متن کاملLocal Rigidity for Anosov Automorphisms
We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1+Hölder conjugate to any C1-small perturbation f such that the derivative Dpf is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d,Z). Examples constructed in ...
متن کاملAnosov Automorphisms of Nilpotent Lie Algebras
Each matrix A in GLn(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra fn,r. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2008
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2007.11.011