Please use this identifier to cite or link to this item:
http://hdl.handle.net/10174/21898
|
Title: | Ergodicity in Umbrella Billiards |
Authors: | Correia, Maria Cox, Christopher Zhang, Hong-Kun |
Keywords: | Ergodicity billiard systems periodic points elliptic islands |
Issue Date: | Sep-2017 |
Publisher: | Isaac Scientific Publishing |
Citation: | M.Correia, C.Cox, H.-K.Zhang (2017) Ergodicity in Umbrella Billiards. New Horizons in Mathematical Physics, Vol.1, No.2 |
Abstract: | We investigate a three-parameter family of billiard tables with circular arc boundaries.
These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and
asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter
is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit
evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing,
the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some
parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new
parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These
may either stabilize or dissipate as the new parameter is increased. We characterize the periodic
points and present evidence of new ergodic examples. |
URI: | https://dx.doi.org/10.22606/nhmp.2017.12004 http://hdl.handle.net/10174/21898 |
ISSN: | ISSN:2521-7402 |
Type: | article |
Appears in Collections: | CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
|