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) |
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Pages (from-to) | 267-273 |
Number of pages | 7 |
Journal | Communications In Mathematical Physics |
Volume | 208 |
Issue number | 2 |
DOIs | |
State | Published - 1999 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics