### Abstract

In a series of important papers [GS1,GS2] Gavrilov and Shilnikov established a topological conjugacy between a surface diffeomorphism having a dissipative hyperbolic periodic point with certain types of quadratic homoclinic tangencies and the full shift on two symbols, thus exhibiting horseshoes near a tangential homoclinic point. In this note, which should be viewed of as an addendum to [BW], we extend this result by showing that such a diffeomorphism with a one-sided isolated homoclinic tangency having any order contact, possible with infinite order contact, possesses a horseshoe near the homoclinic point.

Original language | English (US) |
---|---|

Pages (from-to) | 267-273 |

Number of pages | 7 |

Journal | Communications In Mathematical Physics |

Volume | 208 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1999 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'A geometric criterion for positive topological entropy II: Homoclinic tangencies'. Together they form a unique fingerprint.

## Cite this

Homburg, A. J., & Weiss, H. (1999). A geometric criterion for positive topological entropy II: Homoclinic tangencies.

*Communications In Mathematical Physics*,*208*(2), 267-273. https://doi.org/10.1007/s002200050757