135-178
https://scigraph.springernature.com/explorer/license/
1988-04
http://link.springer.com/10.1007/BF01015324
research_article
en
false
Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors
1988-04-01
The analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems. Prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective Liapunov exponents. For hyperbolic attractors, the latter determines the metric entropies and provides one constraint on the partial dimensions. For nonhyperbolic attractors, there are important modifications. We discuss them for the examples of the logistic and HÃ©non map. We show, in particular, that the generalized dimensions have singularities with noncontinuous derivative, similar to first-order phase transitions in statistical mechanics.
2019-04-10T14:59
articles
readcube_id
3c4334dbb2fc8ac2daa1ed61ce5e76968c083e8c34f46e03fafce05a86e49de3
University of Wuppertal
Physics Department, University of Wuppertal, D-5600, Wuppertal 1, Federal Republic of Germany
University of Zurich
Institute of Theoretical Physics, University of Zurich, CH-8001, Zurich, Switzerland
Pure Mathematics
Grassberger
P.
R.
Badii
1-2
Mathematical Sciences
dimensions_id
pub.1012649108
A.
Politi
0022-4715
1572-9613
Journal of Statistical Physics
10.1007/bf01015324
doi
Istituto Nazionale di Ottica, I-50125, Firenze, Italy
Istituto Nazionale di Ottica
51
Springer Nature - SN SciGraph project