Complexity lower bound for typical right triangular billiards
We provide a lower bound on the complexity function of a typical (in the Lebesgue measure sence) right triangular billiard.
math.DS↗
arXiv subjects
Dmitri Scheglov
Publications and source records attributed to Dmitri Scheglov.
Nonabelian Rauzy-Veech Renormalization
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 cohomological non-equivalence of typical G-extensions over IETs, when G is a compact connected Lie group. This extends a result of Avila and Forni for U(1) to any compact connected Lie group. This is a first result on ergodic theory of nonabelian extensions over IETs.
math.DS↗
Weak mixing for compact Lie extensions of interval exchange transformations
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 function, constant on the intervals, is weakly mixing.
math.DS↗
Complexity growth of a typical triangular billiard is weakly exponential
We provide a weakly exponential complexity upper bound for typical triangular billiards
math.DS↗
Growth of periodic orbits and generalized diagonals for typical triangle billiards
We give an explicit sub-exponential estimate on the growth rate of periodic orbits and generalized diagonals for typical triangle billiards.
math.DS↗
Lower bounds on directional complexity for irrational triangle billiards
We provide explicit lower estimates on the complexity growth in typical directions for a class of irrational triangle billiards
math.DS↗
Splitting time for irrational triangle billiards
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 estimate on this function for some class of angles.
math.DS↗
Canonical metrics in a conformal class
Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.
math.DG↗