2017/03/06 by Siniša Slijepčević, Slijepcevic, Sinisa
Mathematics · Physics and Astronomy · #37A35 #37E40 #37J45 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1703.01815
openalex publication_date 2017/03/06 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We introduce a new measure of instability of area-preserving twist\ndiffeomorphisms, which generalizes the notions of angle of splitting of\nseparatrices, and flux through a gap of a Cantori. As an example of\napplication, we establish a sharp >0 lower bound on the topological entropy in\na neighbourhood of a hyperbolic, unique action-minimizing fixed point, assuming\nonly no topological obstruction to diffusion, i.e. no homotopically non-trivial\ninvariant circle consisting of orbits with the rotation number 0. The proof is\nbased on a new method of precise construction of positive entropy invariant\nmeasures, applicable to more general Lagrangian systems, also in higher degrees\nof freedom.\n