Zobrazeno 1 - 10
of 160
pro vyhledávání: '"37C83"'
Autor:
De Blasi, Irene
This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian potential
Externí odkaz:
http://arxiv.org/abs/2410.15935
We prove that $(a)$ any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse, and $(b)$ any finitely smooth centrally symmetric strictly convex domain, even-rationally integ
Externí odkaz:
http://arxiv.org/abs/2410.12644
We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conj
Externí odkaz:
http://arxiv.org/abs/2410.11117
Autor:
Kontorovich, Alex, Zhang, Xin
We study the set of combinatorial lengths of asymmetric periodic trajectories on the regular pentagon, proving a density-one version of a conjecture of Davis-Lelievre.
Comment: 12 pages, 2 figures
Comment: 12 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2409.10682
Autor:
Dragović, Vladimir, Radnović, Milena
In this work, we introduce a novel concept of magic billiard games and analyse their properties in the case of elliptical boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic, and polynomial forms. A topological d
Externí odkaz:
http://arxiv.org/abs/2409.03158
Autor:
Bruin, Henk, Lukina, Olga
We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb Z$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a skew-function is mo
Externí odkaz:
http://arxiv.org/abs/2408.14079
Autor:
Koval, Illya, Vig, Amir
This paper shows that the wave trace of a bounded and strictly convex planar domain may be arbitrarily smooth in a neighborhood of some point in the length spectrum. In other words, the Poisson relation, which asserts that the singular support of the
Externí odkaz:
http://arxiv.org/abs/2408.09238
Autor:
Knauf, Andreas
We consider the Kepler potential and its relatives $q\mapsto -\|q\|^{-2(1-1/n)}$, $n\in\mathbb{N}$ in arbitrary dimension $d$. We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still re
Externí odkaz:
http://arxiv.org/abs/2408.00877
Autor:
Glutsyuk, Alexey, Matveev, Vladimir S.
In the recent paper arXiv:2405.13258, the first author of this note proved that if a billiard in a convex domain in $\mathbb{R}^n$ is simultaneously projective and Minkowski, then it is the standard Euclidean billiard in an appropriate Euclidean stru
Externí odkaz:
http://arxiv.org/abs/2407.20159
Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic traj
Externí odkaz:
http://arxiv.org/abs/2406.17734