zbMATH — the first resource for mathematics

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

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