## Abstract

The conditions are obtained for the existence of an infinite set of stable periodic

points whose characteristic exponents are separated from zero in the neighborhood of the non-transversal homoclinic point. The conditions are imposed, first of all, on the method of tangency of a stable manifold with an unstable one; however, the proof of the theorem essentially uses the properties of the eigenvalues of the Jacobi matrix at a hyperbolic point.

points whose characteristic exponents are separated from zero in the neighborhood of the non-transversal homoclinic point. The conditions are imposed, first of all, on the method of tangency of a stable manifold with an unstable one; however, the proof of the theorem essentially uses the properties of the eigenvalues of the Jacobi matrix at a hyperbolic point.

Original language | English |
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Pages (from-to) | 380-387 |

Journal | Vestnik St. Petersburg University: Mathematics |

Volume | 52 |

Issue number | 4 |

Early online date | 23 Dec 2019 |

State | Published - 2019 |

## Scopus subject areas

- Mathematics(all)

## Keywords

- multidimentional diffeomophisms
- non-transversal homoclinic point
- Stability
- characteristic exponents separated from zero