Lyapunov exponents and Hodge theory

M. Kontsevich; A. Zorich

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arXiv · hep-th/9701164

Lyapunov exponents and Hodge theory

M. Kontsevich·A. Zorich

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Abstract

We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit integrals over moduli spaces of algebraic curves with additional structures. Moreover, these integrals can be interpreted as correlators in a topological string theory. Also a new analogy arose between ergodic theory and complex algebraic geometry.

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M. Kontsevich, A. Zorich. 1997-01-28. Lyapunov exponents and Hodge theory. https://arxiv.org/abs/hep-th/9701164

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