Geodesic
Symmetric hyperbolic trap
Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 372-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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An arbitrary $C^1$ diffeomorphism $f$ from an open subset $U$ of a Riemannian $m$-manifold $M$, $m\geqslant 2$, to a set $f(U)\subset M$ is considered. Sufficient conditions for the domain $U$ to be a hyperbolic trap are proposed. This means that any set $A\subset U$ satisfying the condition $f(A)=A$ is automatically a hyperbolic set of the diffeomorphism $f$. Moreover, this hyperbolic trap is symmetric in the sense that the conditions for its existence do not change under the passage from $f$ to the inverse map $f^{-1}$.
Keywords: diffeomorphism, manifold, hyperbolic trap.
Mots-clés : invariant set 
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S. D. Glyzin; A. Yu. Kolesov. Symmetric hyperbolic trap. Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 372-387. http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a3/

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