| Full text | |
| Author(s): |
Total Authors: 3
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| 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
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| 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 Opportunities: | Scholarships in Brazil - Post-Doctoral |