Around Anosov-Weil Theory

P. 123–154.

V. Grines, E. Zhuzhoma

The survey is devoted to the exposition of main results of Anosov-Weil Theory that studies nonlocal asymptotic properties of simple curves on a surface with a non-positive constant curvature. This study consists of the lifting these curves to an universal covering and making a “comparison” in a sense with lines of constant geodesic curvature. We review some applications conserning constructions of topological invariants for surface dynamical systems and foliations.

Keywords: Anosov-Weil Theory

Publication based on the results of: Systems and foliations with a complex structure of limit sets (2017)

In book

Contemporary Mathematics

Vol. 692: Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov. , Providence, Rhode Island: American Mathematical Society, 2017.