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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

INFINITELY MANY MODULI OF STABILITY AT THE DISSIPATIVE BOUNDARY OF CHAOS

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Autor(es):
Hazard, P. [1, 2] ; Martens, M. [3] ; Tresser, C. [4]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 - USA
[2] Univ Sao Paulo, IME, Rua Matao, 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[3] SUNY Stony Brook, Inst Math Sci, Stony Brook, NY 11794 - USA
[4] IBM Corp, TJ Watson Res Ctr, Yorktown Hts, NY 10598 - USA
Número total de Afiliações: 4
Tipo de documento: Artigo Científico
Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 370, n. 1, p. 27-51, JAN 2018.
Citações Web of Science: 1
Resumo

In the family of area-contracting Henon-like maps with zero topological entropy we show that there are maps with infinitely many moduli of stability. Thus one cannot find all the possible topological types for non-chaotic area-contracting Henon-like maps in a family with finitely many parameters. A similar result, but for the chaotic maps in the family, became part of the folklore a short time after Henon used such maps to produce what was soon conjectured to be the first non-hyperbolic strange attractor in R-2. Our proof uses recent results about infinitely renormalisable area-contracting Henon-like maps; it suggests that the number of parameters needed to represent all possible topological types for area-contracting Henon-like maps whose sets of periods of their periodic orbits are finite (and in particular are equal to [1, 2,..., 2(n-1)] or an initial segment of this n-tuple) increases with the number of periods. In comparison, among C-k-embeddings of the 2-disk with k >= 1, the maximal moduli number for non-chaotic but non-area-contracting maps in the interior of the set of zero-entropy is infinite. (AU)

Processo FAPESP: 08/10659-1 - Renormalização na família de Hénon
Beneficiário:Peter Edward Hazard
Linha de fomento: Bolsas no Brasil - Pós-Doutorado