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Renormalisation in the Hénon family

Grant number: 08/10659-1
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): May 01, 2009
Effective date (End): November 30, 2011
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:André Salles de Carvalho
Grantee:Peter Edward Hazard
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:06/03829-2 - Dynamic in low dimensions, AP.TEM

Abstract

The renormalization theory for strongly dissipative H\'enon-like mapswas initiated by de Carvalho, Lyubich and Martens in ``Renormalizationin the Henon family I: Universality but Non-Rigidity'' forperiod-doubling combinatorics and by Hazard in ``H\'enon-like Maps andRenormalisation'' for arbitrary stationary combinatorics. In boththese works it was observed that Universality holds in the this twodimensional case, just as in the one-dimensional (unimodal)case. However, it was also observed that, unlike in theone-dimensional case, rigidity fails under the assumption of `tippreservation' and that the invariant Cantor sets for such maps havealmost everywhere unbounded geometry. We wish to continue this studyof infinitely renormalisable maps and their Cantor sets. In particularwe wish to investigate whether infinitely renormalisable H\'enon-likemaps can have bounded geometry Cantor sets and what implications thishas for universality. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
HAZARD, P.; MARTENS, M.; TRESSER, C. INFINITELY MANY MODULI OF STABILITY AT THE DISSIPATIVE BOUNDARY OF CHAOS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 370, n. 1, p. 27-51, JAN 2018. Web of Science Citations: 1.
HAZARD, P. E.; LYUBICH, M.; MARTENS, M. Renormalizable Henon-like maps and unbounded geometry. Nonlinearity, v. 25, n. 2, p. 397-420, FEB 2012. Web of Science Citations: 1.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.