Lan Wen
(Department of Mathematics, Northwestern University,
visiting from Peking University, China)
Minimally Nonhyperbolic Sets for Diffeomorphisms C1 away
from Homoclinic Bifurcations
Abstract
Palis conjectures that diffeomorphisms with a homoclinic tangency or a
heterodimensional cycle are C1 dense in the complement of the
C1 closure of hyperbolic diffeomorphisms. We prove some results
towards the conjecture: C1 away from homoclinic tangencies and
heterodimensional cycles, a C1 generic diffeomorphism must have
no simple minimally nonhyperbolic sets, and any nonsimple minimally nonhyperbolic
set, if exists, must be very special.
|