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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. https://resolver.caltech.edu/CaltechAUTHORS:20200127-141129762

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s002200050833DOIArticle
https://rdcu.be/b0Pz7PublisherFree ReadCube access
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9402946
NSFDMS-9800714
NSFDMS-9304580
NSFDMS-9706875
Subject Keywords:Negative Spectrum
Issue or Number:3
Record Number:CaltechAUTHORS:20200127-141129762
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200127-141129762
Official Citation:Makarov, N. & Smirnov, S. Comm Math Phys (2000) 211: 705. https://doi.org/10.1007/s002200050833
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100951
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jan 2020 19:03
Last Modified:28 Jan 2020 19:03

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