How do the leaves of a closed 1-form wind around a surface? (English) Zbl 0976.37012

Zorich, Anton

Arnold, V. (ed.) et al., Pseudoperiodic topology. With a preface (ix-xii) by V. I. Arnold. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 197(46), 135-178 (1999).

This paper deals with foliations on Riemann surfaces defined by closed 1-forms. The author shows why the interesting topological dynamics of such foliations can be represented by a class of 1-forms obtained as real parts of Abelian differentials. The corresponding “universal constants” are represented in terms of Lyapunov exponents of the Teichmüller geodesic flow on the corresponding moduli space of Abelian differentials.
For the entire collection see [Zbl 0931.00017].

Reviewer: Messoud Efendiev (Berlin)

MSC:

37C85	Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
57R30	Foliations in differential topology; geometric theory
34D08	Characteristic and Lyapunov exponents of ordinary differential equations

Keywords:

universal constants; foliations; Lyapunov exponents; Teichmüller geodesic flow; moduli space of Abelian differentials