TITLE:
Three dimensional dissipative diffeomorphisms with homoclinic tangencies

AUTHOR:
Joan Carles Tatjer

Departament de Matematica Aplicada i Analisi
Universitat de Barcelona
Gran Via 585
08007 Barcelona (Spain)

Email: jcarles@maia.ub.es

ABSTRACT:
Given a two-parameter family of three-dimensional diffeomorphism
$\{ f_{a,b}\}_{a,b},$
with a dissipative (but not sectionally dissipative) saddle fixed point, assume
that
a special type of quadratic homoclinic tangency of the
invariant manifolds exists. Then
there is a return map $f^n_{a,b},$ near  the homoclinic orbit,
for values of the parameter near such tangency and for $n$ large
enough, such that, after
a change of variables and reparametrization depending on $n,$ this return
map tends to a simple quadratic map. This implies the existence of strange
attractors and infinitely many sinks as in other known cases. Moreover, there
appear attracting invariant circles, implying the existence of quasiperiodic
behaviour near the homoclinic tangency.
