Math Seminars
Anton Gorodetski
Cal Tech
On area-preserving Newhouse phenomena
Existence of homoclinic tangencies for a dissipative surface
diffeomorphism leads to amazing phenomenon for perturbations: persistent
tangencies, infinitely many sinks, strange attractors, transitive invariant
sets of full Hausdorff dimension.
In the case of area preserving maps P.Duarte (2000) constructed
persistent tangencies and infinite number of elliptic periodic points. We
use the results by Gelfreich-Lazutkin on splitting of separatrices for the
area preserving Henon family to prove a one parameter version of Duarte's
result and to show the existence of transitive invariant sets of full
Hausdorff dimension for a residual set of parameters. Our interest to the
problem was motivated by applications to celestial mechanics.
This is a joint work with V.Kaloshin.