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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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De Faria, Edson [1] ; Guarino, Pablo [2]
Total Authors: 2
[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Fed Fluminense, Inst Matemat & Estat, BR-24020140 Niteroi, RJ - Brazil
Total Affiliations: 2
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 36, n. 4, p. 1957-1982, APR 2016.
Web of Science Citations: 4

We prove that a C-3 critical circle map without periodic points has zero Lyapunov exponent with respect to its unique invariant Borel probability measure. Moreover, no critical point of such a map satisfies the ColletEckmann condition. This result is proved directly from the well-known real a-prtort bounds, without using Pesin's theory. We also show how our methods yield an analogous result for infinitely renormalizable unimodal maps of any combinatorial type. Finally we discuss an application of these facts to the study of neutral measures of certain rational maps of the Riemann sphere. (AU)

FAPESP's process: 12/06614-8 - Renormalization and rigidity in one-dimensional dynamics
Grantee:Pablo Andrés Guarino Quiñones
Support Opportunities: Scholarships in Brazil - Post-Doctoral