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On "Thermodynamics" of Rational Maps I. Negative Spectrum

Makarov, N. and Smirnov, S. (2000) On "Thermodynamics" of Rational Maps I. Negative Spectrum. Communications in Mathematical Physics, 211 (3). pp. 705-743. ISSN 0010-3616. doi:10.1007/s002200050833.

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We study the pressure spectrum P(t) of the maximal measure for arbitrary rational maps. We also consider its modified version which is defined by means of the variational principle with respect to non-atomic invariant measures. It is shown that for negative values of t, the modified spectrum has all major features of the hyperbolic case (analyticity, the existence of a spectral gap for the corresponding transfer operator, rigidity properties, etc). The spectrum P(t) can be computed in terms of . Their Legendre transforms are the Hausdorff and the box-counting dimension spectra of the maximal measure respectively. This work is closely related to a paper [32] by D. Ruelle.

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Additional Information:© 2000 Springer-Verlag Berlin Heidelberg. Received: 2 August 1999; Accepted: 11 January 2. The author is supported by N.S.F. Grants No. DMS-9402946 and DMS-9800714. The author is supported by N.S.F. Grants No. DMS-9304580 and DMS-9706875.
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Subject Keywords:Negative Spectrum
Issue or Number:3
Record Number:CaltechAUTHORS:20200127-141129762
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Official Citation:Makarov, N. & Smirnov, S. Comm Math Phys (2000) 211: 705.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100951
Deposited By: Tony Diaz
Deposited On:28 Jan 2020 19:03
Last Modified:16 Nov 2021 17:58

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