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Homoclinic tangencies: moduli and topology of separatrices

Published online by Cambridge University Press:  19 September 2008

Rense A. Posthumus  and
Floris Takens
Rense A. Posthumus
Affiliation:
PO Box 800, 9700 AV Groningen, The Netherlands
Floris Takens
Affiliation:
PO Box 800, 9700 AV Groningen, The Netherlands
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Extract

We consider two-dimensional diffeomorphisms φ: M → M. For a fixed point p, i.e., p ∈ M and φ(p) = p, we say that q is homoclinic to p if p ≠ q and if both limi→+∞φi(q) and limi→−∞φi(q) are equal to p.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 369 - 385
Copyright
Copyright © Cambridge University Press 1993

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