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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.)

INFINITELY MANY MODULI OF STABILITY AT THE DISSIPATIVE BOUNDARY OF CHAOS

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Author(s):
Hazard, P. [1, 2] ; Martens, M. [3] ; Tresser, C. [4]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 4
Document type: Journal article
Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 370, n. 1, p. 27-51, JAN 2018.
Web of Science Citations: 1
Abstract

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)

FAPESP's process: 08/10659-1 - Renormalisation in the Hénon family
Grantee:Peter Edward Hazard
Support type: Scholarships in Brazil - Post-Doctorate