925 research outputs found
The limit set of the handlebody set has measure zero
This note fixes a small gap in Kerckhoff's proof that the limit set of the
handlebody set has measure zero.Comment: 3 page
On closing for flows on 2-manifolds
For some full measure subset B of the set of iet's (i.e. interval exchange
transformations) the following is satisfied: Let X be a , , vector field, with finitely many singularities, on a compact
orientable surface M. Given a nontrivial recurrent point of X, the
holonomy map around p is semi-conjugate to an iet If
then there exists a vector field Y, arbitrarily close to X, in
the topology, such that Y has a closed trajectory passing through p.Comment: 7 pages, 1 figur
Ergodic directions for billiards in a strip with periodically located obstacles
We study the size of the set of ergodic directions for the directional
billiard flows on the infinite band with periodically placed
linear barriers of length . We prove that the set of ergodic
directions is always uncountable. Moreover, if is rational
the Hausdorff dimension of the set of ergodic directions is greater than 1/2.
In both cases (rational and irrational) we construct explicitly some sets of
ergodic directions.Comment: The article is complementary to arXiv:1109.458
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