Lyapunov exponents and Hodge theory

Details Lyapunov exponents and Hodge theory Lyapunov exponents and Hodge theory

1997-01-28

arxiv.org/abs/hep-th/9701164v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, Latex, extended version of the talk by one of us (M.K.) at the conference "Mathematical Beauty of Physics", Saclay,

Scientific paper

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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