2 citations · 4 across the 7 of their papers we have counts for
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Complexity lower bound for typical right triangular billiards
Dmitri Scheglov
We provide a lower bound on the complexity function of a typical (in the Lebesgue measure sence) right triangular billiard.
Nonabelian Rauzy-Veech Renormalization
Dmitri Scheglov
For any Lie group G a renormalization map R on the space of simple G-extensions of Interval Exchange Transformations is constructed. R is applied to prove weak mixing and cohomolog…
Weak mixing for compact Lie extensions of interval exchange transformations
Dmitri Scheglov
We prove that for any compact connected Lie group G and a typical interval exchange transformation T, not isomorphic to a rotation, the skew product of T with a typical G-valued fu…
Complexity growth of a typical triangular billiard is weakly exponential
Dmitri Scheglov
We provide a weakly exponential complexity upper bound for typical triangular billiards
Growth of periodic orbits and generalized diagonals for typical triangle billiards
Dmitri Scheglov
We give an explicit sub-exponential estimate on the growth rate of periodic orbits and generalized diagonals for typical triangle billiards.
Lower bounds on directional complexity for irrational triangle billiards
Dmitri Scheglov
We provide explicit lower estimates on the complexity growth in typical directions for a class of irrational triangle billiards
Splitting time for irrational triangle billiards
Dmitri Scheglov
We find an upper estimate for a splitting time of a thin parallel beam for irrational triangle billiards in terms of some number-theoretic function of angles. We provide an upper e…