Geodesic
On Some Sufficient Hyperbolicity Conditions
Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 116-134.

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We consider an arbitrary $C^1$ diffeomorphism $f$ that acts from an open subset $U$ of a Riemannian manifold $M$ of dimension $m$, $m\ge 2$, to $f(U)\subset M$. 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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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. On Some Sufficient Hyperbolicity Conditions. Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 116-134. http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a8/

[1] Afraimovich V., Hsu S.-B., Lectures on chaotic dynamical systems, AMS/IP Stud. Adv. Math., 28, Amer. Math. Soc., Providence, RI, 2003 | DOI | MR | Zbl

[2] D. V. Anosov, Geodesic Flows on Closed Riemann Manifolds with Negative Curvature, Tr. Mat. Inst. Steklova, 90, Nauka, Moscow, 1967 | MR

[3] Proc. Steklov Inst. Math., 90 (1969) | MR

[4] S. D. Glyzin, A. Yu. Kolesov, and N. Kh. Rozov, “The annulus principle in the existence problem for a hyperbolic strange attractor”, Sb. Math., 207:4 (2016), 490–518 | DOI | DOI | MR | Zbl

[5] S. D. Glyzin, A. Yu. Kolesov, and N. Kh. Rozov, “Hyperbolic annulus principle”, Diff. Eqns., 53:3 (2017), 281–301 | DOI | MR | Zbl

[6] Hasselblatt B., Katok A., A first course in dynamics with a panorama of recent developments, Cambridge Univ. Press, Cambridge, 2003 | MR | Zbl

[7] Katok A., Hasselblatt B., Introduction to the modern theory of dynamical systems, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[8] Newhouse S., Palis J., “Bifurcations of Morse–Smale dynamical systems”, Dynamical systems: Proc. Symp. Univ. Bahia (Salvador, 1971), ed. by M.M. Peixoto, Acad. Press, New York, 1973, 303–366 | MR

[9] S. Yu. Pilyugin, Spaces of Dynamical Systems, Inst. Komp'yut. Issled., Moscow, 2008 | MR | MR | Zbl

[10] Spaces of Dynamical Systems, De Gruyter Stud. Math. Phys., 3, De Gruyter, Berlin, 2012 | MR | MR | Zbl

[11] Ya. G. Sinai, “Stochasticity of dynamical systems”, Nonlinear Waves, ed. by A. V. Gaponov-Grekhov, Nauka, Moscow, 1979, 192–212 (in Russian)