Quantitative behavior of nonintegrable systems (IV)
Abstract
In this paper, there are two sections. In Section 7, we simplify the eigenvaluebased surplus shortline method for arbitrary finite polysquare surfaces. This makes it substantially simpler to determine the irregularity exponents of some infinite orbits, and quicker to find the escape rate to infinity of some orbits in some infinite models. In Section 8, our primary goal is to extend the surplus shortline method, both this eigenvaluebased version as well as the eigenvaluefree version, for application to a large class of 2dimensional flat dynamical systems beyond polysquares, including all Veech surfaces, and establish timequantitative equidistribution and timequantitative superdensity of some infinite orbits in these new systems.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.12038
 Bibcode:
 2020arXiv201212038B
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Mathematics  Dynamical Systems;
 Mathematics  Number Theory;
 11K38;
 37E35
 EPrint:
 120 pages, 124 figures