Naslov
A new measure of instability and topological entropy of area-preserving twist diffeomorphisms

Autori
Slijepčević, Siniša

Izvornik
Ergodic theory & dynamical systems (0143-3857) 21 (2017); 117-141

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Twist maps ; topological entropy ; metric entropy ; separatrix splitting ; variational techniques

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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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