Izvorni znanstveni članak
https://doi.org/10.21857/m8vqrt0z59
A new measure of instability and topological entropy of area-preserving twist diffeomorphisms
Siniša Slijepčević
orcid.org/0000-0001-5600-0171
; Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
Sažetak
We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp > 0 lower bound on the topological entropy in a neighbourhood of a hyperbolic, unique action-minimizing fixed point, assuming only no topological obstruction to diffusion, i.e. no homotopically non-trivial invariant circle consisting of orbits with the rotation number 0. The proof is based on a new method of precise construction of positive entropy invariant measures, applicable to more general Lagrangian systems, also in higher degrees of freedom.
Ključne riječi
Twist maps; topological entropy; metric entropy; separatrix splitting; variational techniques
Hrčak ID:
186434
URI
Datum izdavanja:
13.9.2017.
Posjeta: 1.067 *