Topological methods in surface dynamics: from the Hénon family to torus rotation sets

• Grant number: 11/17581-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: July 15, 2012 - July 14, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: André Salles de Carvalho
• Grantee: André Salles de Carvalho
• Visiting researcher: Toby Hall
• Visiting researcher institution: University of Liverpool, England
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This proposal seeks to: - Build on long-standing collaborative work between de Carvalho and Hall, partly in collaboration with other researchers at IME-USP such as Tal, Zanata, and Mendoza, in the following projects: a) Continuation of the study of the transition to chaos in dimension 2, with emphasis on the completion of the family of unimodal generalized pseudo-Anosovs, and the construction of generalized pseudo-Anosovs with different underlying train tracks. b) Study of the rotation sets of torus homeomorphisms, in particular exotic rotation sets arising in pruning families. c) Numerical exploration of the Henon family, with a view to extending the regions of parameter space in which the Pruning Front Conjecture can be shown to hold.- Strengthen Hall's links with researchers and graduate students in dynamical systems both at USP and more widely.- Extend and develop links between USP and the University of Liverpool for the exchange of graduate students under the Ciência sem fronteiras program. (AU)

Scientific publications

(5)

(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)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. ON DIGIT FREQUENCIES IN beta-EXPANSIONS. Transactions of the American Mathematical Society, v. 368, n. 12, p. 8633-8674, DEC 2016. (11/17581-0, 10/09667-0)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Symbol ratio minimax sequences in the lexicographic order. Ergodic Theory and Dynamical Systems, v. 35, n. 8, p. 2371-2396, DEC 2015. (11/17581-0, 10/09667-0)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. New rotation sets in a family of torus homeomorphisms. INVENTIONES MATHEMATICAE, v. 204, n. 3, p. 895-937, JUN 2016. (11/17581-0, 10/09667-0)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. ON DIGIT FREQUENCIES IN beta-EXPANSIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 368, n. 12, p. 42-pg., 2016-12-01. (11/17581-0, 10/09667-0)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Symbol ratio minimax sequences in the lexicographic order. Ergodic Theory and Dynamical Systems, v. 35, p. 26-pg., 2015-12-01. (11/17581-0, 10/09667-0)