Dimensions of Attractors in Pinched Skew Products

被引：0
作者：
M. Gröger
T. Jäger
机构：
[1] Universität Bremen,Department of Mathematics
[2] TU Dresden,Department of Mathematics
来源：
Communications in Mathematical Physics | 2013年 / 320卷
关键词：
Lyapunov Exponent; Invariant Measure; Hausdorff Dimension; Global Attractor; Hausdorff Measure;
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摘要：
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.
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页码：101 / 119
页数：18
相关论文
共 33 条
[1]  
Grebogi C.(1984)Strange attractors that are not chaotic Physica D 13 261-268
[2]  
Ott E.(2002)Global attractors of pinched skew products Dyn. Syst. 17 287-294
[3]  
Pelikan S.(1996)A note on strange nonchaotic attractors Fund. Math. 151 139-148
[4]  
Yorke J.A.(2001)Strange nonchaotic attractors Int. J. Bif. Chaos 11 291-309
[5]  
Glendinning P.(2006)Strange non-chaotic attractors in Harper maps Chaos 16 033127-106
[6]  
Keller G.(2009)The creation of strange non-chaotic attractors in non-smooth saddle-node bifurcations Mem. Am. Math. Soc. 945 1-172
[7]  
Prasad A.(1989)Dimensions of strange nonchaotic attractors Phys. Lett. A 137 167-510
[8]  
Negi S.S.(2007)On the structure of strange nonchaotic attractors in pinched skew products Erg. Th. Dyn. Syst. 27 493-1045
[9]  
Ramaswamy R.(2005)Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations Erg. Th. Dyn. Syst. 25 1015-442
[10]  
Haro A.(2005)Dynamics of the quasiperiodic Schrödinger cocycle at the lowest energy in the spectrum Commun. Math. Phys. 272 397-161
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