REAL BOUNDS AND LYAPUNOV EXPONENTS

Autor(es)

De Faria, Edson ^[1] ; Guarino, Pablo ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 36, n. 4, p. 1957-1982, APR 2016.
• Citações Web of Science: 4

Resumo

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)

• Processo FAPESP: 12/06614-8 - Renormalização e rigidez em dinâmica unidimensional
• Beneficiário: Pablo Andrés Guarino Quiñones
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado