Exceptional sets for geodesic flows of noncompact manifolds

For a geodesic flow on a negatively curved Riemannian manifold \(M\) and some subset \(A\subset T^1M\), we study the limit \(A\)-exceptional set, that is the set of points whose \(\omega\)-limit do not intersect \(A\). We show that if the topological \(\ast\)-entropy of \(A\) is smaller than the top...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Gelfert, Katrin, Riquelme, Felipe
Format: Article
Language:English
Subjects:
Entropy
Manifolds (mathematics)
Riemann manifold
Topology
Online Access:Get full text
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Summary:For a geodesic flow on a negatively curved Riemannian manifold \(M\) and some subset \(A\subset T^1M\), we study the limit \(A\)-exceptional set, that is the set of points whose \(\omega\)-limit do not intersect \(A\). We show that if the topological \(\ast\)-entropy of \(A\) is smaller than the topological entropy of the geodesic flow, then the limit \(A\)-exceptional set has full topological entropy. Some consequences are stated for limit exceptional sets of invariant compact subsets and proper submanifolds.
ISSN:2331-8422