## American Mathematical Society TranslationsTranslations of articles on mathematics appearing in various Russian mathematical serials. |

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### Contents

A G Kusnirenko Problems in the general theory of dynamical systems on | 1 |

A B Katok Dynamical systems with hyperbolic structure | 97 |

KyuiHHpeHKo A F 3anamt o6meii TeopHH AHHaMHiecKHX cucreM | 124 |

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### Common terms and phrases

action analogous analytic Anosov diffeomorphisms assertion automorphism behavior Chazy compact consider consists construction coordinates corresponding curves defined definition denote Diff diffeo diffeomor differential equations dynamical systems eigenvalues everywhere dense Example exists families of e-trajectories Figure finite number fixed point x0 flow pt function geodesic flow Hence homeomorphism homoclinic point hyperbolic fixed point hyperbolic set integral intersection invariant set invariant with respect Kusnirenko's lectures Lemma locally maximal hyperbolic mapping Math matrix maximal hyperbolic set morphism motion nonempty obtain open set orbit partially hyperbolic periodic points periodic trajectories phase space phism plane point x G proof proved Riemannian metric separatrices sequence Smale smooth solutions stable and unstable stable manifold structurally stable subset subspaces sufficiently small symbolic dynamics tangent theorem on families theorem on stable theory three-body problem tion topologically conjugate topologically transitive torus transversal two-dimensional vector field velocity Ws(x zero