DC Field | Value | Language |
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dc.contributor.author | Choe, Geon Ho | ko |
dc.date.accessioned | 2013-03-03T11:48:03Z | - |
dc.date.available | 2013-03-03T11:48:03Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2003-05 | - |
dc.identifier.citation | NONLINEARITY, v.16, pp.883 - 896 | - |
dc.identifier.issn | 0951-7715 | - |
dc.identifier.uri | http://hdl.handle.net/10203/78529 | - |
dc.description.abstract | A point x in [0, 1] is represented as a binary expansion, i.e. it is identified with an infinite binary sequence of 0 and I. Given a map T satisfying 0 less than or equal to T (x) less than or equal to 1 for 0 less than or equal to x less than or equal to 1, we iterate the map T until the first n bits in x recur as the first n bits in the K(n)th iterate T-Kn(x) for some K-n = K-n (x). We call K-n (x) the nth recurrence time of x. More precisely, put E-n,E-j = [ (j - 1)/2(n), j/2(n)), 1 less than or equal to j less than or equal to 2(n), and let E-n(x) be one of the intervals E-n,E-j containing x. Then K-n(x) = min{j greater than or equal to 1 : T-j(x) is an element of E-n(x)}. For higher dimensional cases we define the recurrence time using subcubes instead of subintervals. For a wide class of T including Henon mappings we present two conjectures: first, if T is ergodic and has positive entropy, then the sequence of averages of (log(2) K-n)/n monotonically converges to the Hausdorff dimension as n --> infinity. Second, the values of KnPn are exponentially distributed as n --> infinity where P-n(x) is the measure of E-n(x). To support our conjectures computer simulations are presented. | - |
dc.language | English | - |
dc.publisher | IOP PUBLISHING LTD | - |
dc.subject | HAUSDORFF DIMENSION | - |
dc.subject | LYAPUNOV EXPONENTS | - |
dc.subject | DATA-COMPRESSION | - |
dc.subject | DYNAMIC-SYSTEMS | - |
dc.subject | LIMIT LAW | - |
dc.subject | TRAJECTORIES | - |
dc.subject | ENTROPY | - |
dc.title | A universal law of logarithm of the recurrence time | - |
dc.type | Article | - |
dc.identifier.wosid | 000183174000007 | - |
dc.identifier.scopusid | 2-s2.0-0242277034 | - |
dc.type.rims | ART | - |
dc.citation.volume | 16 | - |
dc.citation.beginningpage | 883 | - |
dc.citation.endingpage | 896 | - |
dc.citation.publicationname | NONLINEARITY | - |
dc.contributor.localauthor | Choe, Geon Ho | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | HAUSDORFF DIMENSION | - |
dc.subject.keywordPlus | LYAPUNOV EXPONENTS | - |
dc.subject.keywordPlus | DATA-COMPRESSION | - |
dc.subject.keywordPlus | DYNAMIC-SYSTEMS | - |
dc.subject.keywordPlus | LIMIT LAW | - |
dc.subject.keywordPlus | TRAJECTORIES | - |
dc.subject.keywordPlus | ENTROPY | - |
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