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.