Symmetric periodic orbits in families of interval exchange maps persist for small perturbations and are found via one-dimensional searches along symmetry lines, with bifurcations connected to the standard map viewed as a two-interval case.
Lyapunov exponents and Hodge theory
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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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2026 1verdicts
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Perturbed Families of Symmetric Interval Exchange Maps
Symmetric periodic orbits in families of interval exchange maps persist for small perturbations and are found via one-dimensional searches along symmetry lines, with bifurcations connected to the standard map viewed as a two-interval case.