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DTSTAMP:20170720T203430Z
UID:1e4f9ee3-3106-48df-9823-599544f5af0f
DTSTART:20170302T151500
DTEND:20170302T161500
DESCRIPTION:We study the Lyapunov exponents Λ(x) for Markov dynamics as a f
unction 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 nu
mbers the corresponding function ΛX is convex and strictly monotonic. The k
ey step is using the relation of Markov numbers with hyperbolic structures
on punctured torus\, going back to D. Gorshkov and H. Cohn\, and\, more pre
cisely\, the recent result by V. Fock\, who combined this with Thurston’s l
amination ideas. The talk is based on joint work with K. Spalding.
LOCATION:ETH Zürich\, Zentrum HG G 43
ORGANIZER:
SUMMARY:Lyapunov spectrum for Markov dynamics and hyperbolic structures
URL:https://www.math.ethz.ch/news-and-events/events/research-seminars/talks
-in-mathematical-physics.html
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