On Some Sufficient Hyperbolicity Conditions

—We consider an arbitrary C 1 diffeomorphism f that acts from an open subset U of a Riemannian manifold M of dimension m , m ≥ 2, to f (U) ⊂ M . Let A be a compact f -invariant (i.e., f ( A ) = A ) subset in U . We propose various sufficient conditions under which A is a hyperbolic set of f .

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2020, Vol.308 (1), p.107-124
Main Authors: Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format: Article
Language:English
Subjects:
Isomorphism
Mathematics
Mathematics and Statistics
Riemann manifold
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Summary:—We consider an arbitrary C 1 diffeomorphism f that acts from an open subset U of a Riemannian manifold M of dimension m , m ≥ 2, to f (U) ⊂ M . Let A be a compact f -invariant (i.e., f ( A ) = A ) subset in U . We propose various sufficient conditions under which A is a hyperbolic set of f .
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543820010095