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  • 1
    Electronic Resource
    Electronic Resource
    The dimension spectrum of some dynamical systems (1987)
    Springer
    Journal of statistical physics 47 (1987), S. 609-644 
    Details
    ISSN: 1572-9613
    Keywords: Hausdorff dimension spectrum ; partition function ; period doubling ; critical circle map ; universality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze the dimension spectrum previously introduced and measured experimentally by Jensen, Kadanoff, and Libchaber. Using large-deviation theory, we prove, for some invariant measures of expanding Markov maps, that the Hausdorff dimensionf(α) of the set on which the measure has a singularity α is a well-defined, concave, and regular function. In particular, we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number. We also show in these particular cases that the functionf is universal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01206149
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  • 2
    Electronic Resource
    Electronic Resource
    The dimension spectrum of axiom a attractors (1990)
    Springer
    Journal of statistical physics 58 (1990), S. 923-937 
    Details
    ISSN: 1572-9613
    Keywords: Hyperbolic attractors ; Hausdorff dimension spectrum ; thermodynamic formalism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Some rigorous results on the dimension spectrum of expanding Markov maps of the interval are extended to Axiom AC 2 diffeomorphisms of a compact two-dimensional manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01026557
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