### 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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

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

}

*Communications In Mathematical Physics*, vol. 208, no. 2, pp. 267-273. https://doi.org/10.1007/s002200050757

**A geometric criterion for positive topological entropy II : Homoclinic tangencies.** / Homburg, Ale Jan; Weiss, Howard.

Research output: Contribution to journal › Review article

TY - JOUR

T1 - A geometric criterion for positive topological entropy II

T2 - Homoclinic tangencies

AU - Homburg, Ale Jan

AU - Weiss, Howard

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033235153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033235153&partnerID=8YFLogxK

U2 - 10.1007/s002200050757

DO - 10.1007/s002200050757

M3 - Review article

AN - SCOPUS:0033235153

VL - 208

SP - 267

EP - 273

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -