|Table of Contents|

Upper Estimate on Multifractal Spectrum of Local Dimension for Recurrence Time(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2011年01期
Page:
29-34
Research Field:
数学
Publishing date:

Info

Title:
Upper Estimate on Multifractal Spectrum of Local Dimension for Recurrence Time
Author(s):
Yan Zhenzhen1; Chen Ercai2; Li Lei1
1.School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210003,China 2. School ofM athem at ical Sciences, Nanj ing Norm alUn iversity, Nan jing 210046, Ch ina
Keywords:
m ultifracta l ana lysis;  loca l d im ensions for recurrence time;  H ausdor ff dim ension;  ( q;  τ)-dim ension
PACS:
O211.6
DOI:
-
Abstract:
Th is paper is dedica ted to study mu ltifracta l decom po sition of loca l dim ens ion fo r Po incar?recurrence tim e. The uppe r estim ate on m ultifracta l spec trum w ith H ausdorff d im ension o f local dim ens ion for Po incar?recurrence tim e is ob tained.

References:

[ 1] H alsey T C, JensenM H, Kadano ff L, e t a .l Fracta lmeasures and the ir singular itis: the characte rization of strange sets[ J]. Phys Rev A, 1986, 34( 3): 1 141-1 151.
[ 2] Lau K S. Sel-f sim ilarity, Lp-spectrum for recurren t IFS attractors[ J]. Non linear ity, 1992, 6: 337-348.
[ 3] O lsen O. Se l-f affine mu ltifracta l S ie rpinsk i spong es in Rd [ J]. Pac ific JM a th, 1998, 183( 1) : 143-199.
[ 4] Fa lcone rK J. Techn iques in Fracta l Geom etry[M ] . Chrchester: W iley, 1997.
[ 5] Pesin Y. Dim ension Theory in Dynam ica l System [M ]. Ch icago: Un iv o f Ch icago Press, IL, 1997.
[ 6] Takens F, Verb itski E. Genera lmu ltifrac tal ana lysis of loca l entrop ies[ J]. Fundam entaM a them a ticae, 2000, 165( 2): 203- 237.
[ 7] 严珍珍, 陈二才. 局部熵的高维重分形分析[ J]. 系统科学与数学, 2008, 28( 1): 40-50.
[ 8] Yan Z Z, Chen E C. Uppe r estim a tes on the higher-dim ens iona lmu ltifracta l spectrum o f lo ca l entropy[ J]. No rtheastM ath J, 2008, 24( 6): 471-484.
[ 9] Afra im ovich V, Chazottes J, Sausso l B. Loca l d im ensions for Po incar?recurrences[ J]. E lec tron ic Research Announcem ents o fAm erM ath Soc, 2000, 6: 64-74.
[ 10] A fraim ov ich V, Chazo ttes J, Sausso l B. Po intw ise dim ensions fo r Po incar?recurrences assoc iated w ith m aps and flows[ J]. D iscrete and Continuous Dynam ical Sy stem s A, 2003, 9: 263-280.
[ 11] Yan Z Z, Chen E C. Mu ltifracta l analysis of lo ca l entropies for recurrence tim e[ J] . Chaos, So litons& Fracta ls, 2007, 33 ( 5): 1 584-1 591.
[ 12] Barre ira L, Saussol B. H ausdo rff d imension of m easure v ia Po incar?recurrence[ J] . Comm M ath Phys, 2001, 219: 443- 463.
[ 13] O lsen L. A mu ltifrac tal fo rm alism [ J]. Advances inM athema tics, 1995, 116( 1): 82-196.

Memo

Memo:
-
Last Update: 2013-04-11