Lyapunov spectrum for Markov dynamics and hyperbolic structures
2.03.2017
| Date | 2.03.2017 |
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| Time | 15:15 |
| Place |
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| Speaker | Alexander Veselov |
| Area of expertise | Physics |
| Host | Dep. Physik |
| Contact | |
| Abstract | We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x ∈ RP1 on a binary planar tree, describing the growth of Markov triples and their ``tropical" version - Euclid triples. We show that the corresponding Lyapunov spectrum is [0, ln φ], where φ is the golden ratio, and prove that on the set X of the most irrational numbers the corresponding function ΛX is convex and strictly monotonic. The key step is using the relation of Markov numbers with hyperbolic structures on punctured torus, going back to D. Gorshkov and H. Cohn, and, more precisely, the recent result by V. Fock, who combined this with Thurston’s lamination ideas. The talk is based on joint work with K. Spalding. |