Existence of homoclinic intersections
Lan Wen
Department of Mathematics
Northwestern University and Peking University, China
Palis conjectures that every diffeomorphism can be C1 approximated either by a Morse-Smale diffeomorphisms, or by one that has a transverse homoclinic intersection (a horseshoe). Briefly, the conjecture states that every diffeomorphism can be C1 approximated either by one that is very simple, or by one that is very complicated. In this talk we report some recent progress about this conjecture.