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Dynamic in low dimensions

Grant number: 06/03829-2
Support type:Research Projects - Thematic Grants
Duration: December 01, 2006 - November 30, 2011
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:André Salles de Carvalho
Grantee:André Salles de Carvalho
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Co-Principal Investigators:Albert Meads Fisher ; Edson de Faria ; Edson Vargas ; Salvador Addas Zanata
Assoc. researchers:Eduardo Colli ; Fábio Armando Tal ; Pedro Antonio Santoro Salomão ; Salvador Addas Zanata
Associated grant(s):11/01830-1 - Dynamics and contact topology, AV.EXT
11/50128-8 - Charles Tresser | IBM - Estados Unidos, AV.EXT
10/09667-0 - Topological methods in low-dimensional dynamics, AV.EXT
09/17358-0 - The transition from finite to infinite measures in dynamical systems, AV.EXT
Associated scholarship(s):11/19948-9 - Existence o finite energy foliations on symplectizations of contact manifolds, BE.PQ
11/12133-0 - Infinite measures, self-similar actions and continued fractions in ergodic theory, BE.PQ
10/20159-6 - Pruning theory and dynamics of the complex Hénon family, BP.PD
+ associated scholarships 09/16234-5 - Geometric Cone-Structures on Manifolds of dimension 2 and 3, BP.PD
09/08367-5 - Physical measures for critical covering maps of the circle, BP.DR
08/10659-1 - Renormalisation in the Hénon family, BP.PD
08/10059-4 - Ergodic Optimization, BP.PD
07/08114-4 - Dynamics of Fuchsians groups, BP.IC - associated scholarships


The modern theory of dynamical systems started with the work of Poincaré and, since then, grew into a mature and very active branch of mathematical research. The main goal of this project is to further the study of the following areas of dynamical systems theory: - Hamiltonian systems with two degrees of freedom, their dynamical and topological aspects. - Polinomial differential equations on the plane and the 16th Problem of Hilbert. - Two¬dimensional homeomorphisms and diffeomorphisms such as Hénon maps and twits maps of the annulus. Renormalization theory in dimensions 1 and 2. - Interval endomorphisms (e.g., delicate analytic questions such as decay of geometry and existence of invariant measures); critical circle mappings; renormalization and parameter space. - Teichmueller theory and connections with low dimensional dynamics. - Differentiable ergodic theory. While dynamical systems theory developed it also moved away from other branchs of mathematics which were also started by Poincaré: symplectic geometry and topology. Another important goal of this project is to look for and to develop connections between these areas to the point of making it possible to use techniques of each area to attack problems of the other. (AU)

Scientific publications (9)
(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)
DE CARVALHO, ANDRE; HALL, TOBY. Riemann surfaces out of paper. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 108, n. 3, p. 541-574, MAR 2014. Web of Science Citations: 0.
BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Inverse limits as attractors in parameterized families. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. 45, n. 5, p. 1075-1085, OCT 2013. Web of Science Citations: 2.
DE FARIA, EDSON; TRESSER, CHARLES. Bell Inequality Violations Under Reasonable and Under Weak Hypotheses. Physical Review Letters, v. 110, n. 26 JUN 28 2013. Web of Science Citations: 1.
DE CARVALHO, ANDRE; HALL, TOBY. Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences. GEOMETRY & TOPOLOGY, v. 16, n. 4, p. 1881-1966, 2012. Web of Science Citations: 3.
DE MELO, WELINGTON; SALOMAO, PEDRO A. S.; VARGAS, EDSON. A full family of multimodal maps on the circle. Ergodic Theory and Dynamical Systems, v. 31, n. 5, p. 1325-1344, OCT 2011. Web of Science Citations: 2.
HRYNIEWICZ, UMBERTO; SALOMAO, PEDRO A. S. ON THE EXISTENCE OF DISK-LIKE GLOBAL SECTIONS FOR REEB FLOWS ON THE TIGHT 3-SPHERE. Duke Mathematical Journal, v. 160, n. 3, p. 415-465, 2011. Web of Science Citations: 11.
DE CARVALHO, ANDRE; HALL, TOBY. Paper surfaces and dynamical limits. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, v. 107, n. 32, p. 14030-14035, AUG 10 2010. Web of Science Citations: 1.
DE CARVALHO, ANDRE; HALL, TOBY; VENZKE, RUPERT. ON PERIOD MINIMAL PSEUDO-ANOSOV BRAIDS. Proceedings of the American Mathematical Society, v. 137, n. 5, p. 1771-1776, 2009. Web of Science Citations: 0.

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