Polynomial approximations of symplectic dynamics and richness of chaos in non-hyperbolic area-preserving maps

By D. Turaev. 2003

66 citations recorded by the source corpus.

It is shown that every symplectic diffeomorphism of R2n can be approximated, in the C∞-topology, on any compact set, by some iteration of some map of the form (x,y)(y+η,−x+∇V(y)) where xRn, yRn, and V is a polynomial Rn→R and ηRn is a constant vector. For the case of area-preserving maps (i.e. n = 1), it is shown how this result can be applied to prove that Cr-universal maps (a map is universal if its iterations approximate dynamics of all Cr-smooth area-preserving maps altogether) are dense in the Cr-topology in the Newhouse regions.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9b3a4b1356ee465cef9ee95229b3c729615f3cb1