Convergence to alpha-stable Levy motion for chaotic billiards with several cusps at flat points

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 124
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorJung, Paul Heajoonko
dc.contributor.authorPene, Francoiseko
dc.contributor.authorZhang, Hong-Kunko
dc.date.accessioned2020-01-30T03:20:08Z-
dc.date.available2020-01-30T03:20:08Z-
dc.date.created2020-01-03-
dc.date.issued2020-02-
dc.identifier.citationNONLINEARITY, v.33, no.2, pp.807 - 839-
dc.identifier.issn0951-7715-
dc.identifier.urihttp://hdl.handle.net/10203/271884-
dc.description.abstractWe consider billiards with several possibly non-isometric and asymmetric cusps at flat points; the case of a single symmetric cusp was studied previously in Zhang (2017 Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov (Contemporary Mathematics vol 698) (Providence, RI: American Mathematical Society) pp 287-316) and Jung and Zhang (2018 Ann. Henri Poincare 19 3815-53). In particular, we show that properly normalized Birkhoff sums of Holder observables, with respect to the billiard map, converge in Skorokhod's M-1-topology to an -stable Levy motion, where depends on the 'curvature' of the flattest points and the skewness parameter depends on the values of the observable at those same points. Previously, Jung and Zhang (2018 Ann. Henri Poincare 19 3815-53) proved convergence of the one-point marginals to totally skewed -stable distributions for a symmetric cusp. The limits we prove here are stronger, since they are in the functional sense, but also allow for more varied behaviour due to the presence of multiple cusps. In particular, the general limits we obtain allow for any skewness parameter, as opposed to just the totally skewed cases. We also show that convergence in the stronger J(1)-topology is not possible.-
dc.languageEnglish-
dc.publisherIOP PUBLISHING LTD-
dc.titleConvergence to alpha-stable Levy motion for chaotic billiards with several cusps at flat points-
dc.typeArticle-
dc.identifier.wosid000507282500004-
dc.type.rimsART-
dc.citation.volume33-
dc.citation.issue2-
dc.citation.beginningpage807-
dc.citation.endingpage839-
dc.citation.publicationnameNONLINEARITY-
dc.identifier.doi10.1088/1361-6544/ab5148-
dc.contributor.localauthorJung, Paul Heajoon-
dc.contributor.nonIdAuthorPene, Francoise-
dc.contributor.nonIdAuthorZhang, Hong-Kun-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthordynamical systems-
dc.subject.keywordAuthorbilliards-
dc.subject.keywordAuthorstable law-
dc.subject.keywordAuthorstatistical properties-
dc.subject.keywordPlusWEAK-CONVERGENCE-
dc.subject.keywordPlusDECAY-
dc.subject.keywordPlusSUMS-
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0