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2020•Proceedings of the Steklov Institute of MathematicsRequires access

On Some Sufficient Hyperbolicity Conditions

Sergey Dmitrievich Glyzin, A. Yu. Kolesov, Nikolai Khristovich Rozov

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Abstract

Abstract—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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Abstract—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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Available abstract

Abstract—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 .

Key concepts: Diffeomorphism, Mathematics, Riemannian manifold, Invariant (physics), Pure mathematics, Manifold (fluid mechanics), Dimension (graph theory), Set (abstract data type)

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