ISSN:
1572-9613
Keywords:
Dynamical systems
;
generalized dimensions and entropies
;
Liapunov exponents
;
scaling functions
;
hyperbolicity
;
phase transitions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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 Hénon map. We show, in particular, that the generalized dimensions have singularities with noncontinuous derivative, similar to first-order phase transitions in statistical mechanics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01015324
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