INFINITELY MANY MODULI OF STABILITY AT THE DISSIPATIVE BOUNDARY OF CHAOS

Autor(es)

Hazard, P. ^{[1, 2]} ; Martens, M. ^[3] ; Tresser, C. ^[4]

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

• 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