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pro vyhledávání: '"11K38, 37E35"'
Autor:
Beck, J., Chen, W. W. L.
In this paper, we show that billiard orbits in rational polygons and geodesics on translation surfaces exhibit super-fast spreading, an optimal time-quantitative majority property about the corresponding linear flow that implies uniformity in almost
Externí odkaz:
http://arxiv.org/abs/2201.01959
Autor:
Beck, J., Chen, W. W. L.
We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimensional versions of results established in our earlier investigation of the discrete 2-circle problem studied in 1969 by Veech. Whereas the
Externí odkaz:
http://arxiv.org/abs/2107.02289
An interesting result of Veech more than 50 years ago is a parity, or mod $2$, version of the Kronecker--Weyl equidistribution theorem concerning the irrational rotation sequence $\{q\alpha\}$, $q=0,1,2,3,\ldots.$ If $\alpha$ is badly approximable an
Externí odkaz:
http://arxiv.org/abs/2106.14001
Autor:
Beck, J., Chen, W. W. L.
We introduce a new method to establish time-quantitative density in flat dynamical systems. First we give a shorter and different proof of our earlier result that a half-infinite geodesic on an arbitrary finite polysquare surface P is superdense on P
Externí odkaz:
http://arxiv.org/abs/2104.09930
Autor:
Beck, J., Chen, W. W. L.
The continuous version of a fundamental result of Khinchin says that a half-infinite torus line in the unit square $[0,1]^2$ exhibits superdensity, which is a best form of time-quantitative density, if and only if the slope of the geodesic is a badly
Externí odkaz:
http://arxiv.org/abs/2104.09089
Autor:
Beck, Jozsef, Chen, William
Given any rectangular polyhedron 3-manifold $P$ tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in $P$.
Com
Com
Externí odkaz:
http://arxiv.org/abs/2012.09464
In this paper, there are two sections. In Section 7, we simplify the eigenvalue-based surplus shortline method for arbitrary finite polysquare translation surfaces. This makes it substantially simpler to determine the irregularity exponents of some i
Externí odkaz:
http://arxiv.org/abs/2012.12038
The main purpose of part (III) is to give explicit geodesics and billiard orbits in polysquares that exhibit time-quantitative density. In many instances, we can even establish a best possible form of time-quantitative density called superdensity. We
Externí odkaz:
http://arxiv.org/abs/2006.06213
Autor:
Beck, J., Chen, W. W. L.
We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimensional versions of results established in our earlier investigation of the discrete 2-circle problem studied in 1969 by Veech. Whereas the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ea9e463ab92410a32dcee0a89275dbe
http://arxiv.org/abs/2107.02289
http://arxiv.org/abs/2107.02289