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Low dimensional dynamics

Grant number: 11/16265-8
Support Opportunities:Research Projects - Thematic Grants
Duration: April 01, 2012 - September 30, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Edson Vargas
Grantee:Edson Vargas
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Pesquisadores principais:
( Últimos )
Albert Meads Fisher ; Clodoaldo Grotta Ragazzo ; Edson de Faria ; Fábio Armando Tal ; Pedro Antonio Santoro Salomão ; Salvador Addas Zanata
Pesquisadores principais:
( Antigos )
Edson Vargas
Associated researchers:Eduardo Colli ; Manuel Valentim de Pera Garcia ; Ricardo dos Santos Freire Júnior ; Rodrigo Bissacot Proença
Associated grant(s):17/10106-1 - Ergodicity and asymmetry in one dimensional dynamics, AV.EXT
15/21049-3 - Morse-Smale theory adapted to the study of non-autonomous systems, AV.EXT
15/20162-0 - Approximate hyperbolic measures by Bernoulli measures, AV.EXT
+ associated grants 15/17909-7 - Regularity and the boundary of chaos, AV.EXT
15/15088-6 - Limits of dynamical systems, AV.EXT
15/09133-9 - Lyapunov exponents and irregular sets for unimodal dynamics, AV.EXT
15/00037-7 - Self-similarity and the transition from finite to infinite measures in dynamical systems, AV.EXT
14/08628-1 - International Congress of Mathematicians, AR.EXT
12/19995-0 - Visit of professor Charles Tresser to IME-USP, AV.EXT
12/04511-7 - Ergodic properties for flows, AV.EXT - associated grants
Associated scholarship(s):16/25970-0 - Renormalization of asymptotically holomorphic systems, BE.PQ
16/20565-0 - Embbeded contact homology and Reeb dynamics, BP.PD
16/06262-5 - Topological methods and dynamics in dimension 2, BE.PQ
+ associated scholarships 16/16012-6 - Renormalizable correspondences and Hausdorff dimension, BP.PD
16/04687-9 - Dynamics and geometry in dimensions 1, 2 and 3, BE.PQ
16/10466-5 - Reeb flows and finite energy foliations, BP.DR
16/08518-7 - Gibbs Measures and Phase Transitions, BE.PQ
14/25679-9 - Open dynamical systems, beta expansions and symbolic dynamics, BP.PD
14/09418-0 - Low dimensional multimodal maps, BP.PD
14/12872-5 - Transitive and entropy for homeomorphisms of surface, BP.DR
14/10637-9 - Combinatorial Problems in Ferromagnetic Models, BP.DR
14/08113-1 - Systems of transverse sections in classical mechanics, BP.PD
14/11434-4 - Dynamics of interval multimodal maps, BP.IC
13/20480-7 - Parabolic phenomena in complex dynamics, BP.PD
13/15022-0 - Stability properties in dynamical systems, BP.IC
13/13280-1 - Stability properties in dynamical systems, BP.IC
12/13615-0 - Hyperbolic 3-Manifolds and Forcing of Surface Automorphisms, BP.PD
12/07708-6 - Classical mechanics and differential equations, BP.IC
12/06368-7 - Large deviations principles for Gibbs-Equilibrium measures on countable Markov shifts at zero temperature, BP.DR
12/05974-0 - Dynamics and Geometry of 3-Manifolds, BP.DR
11/01482-3 - Dynamics with critical points of mixed criticality, BP.PD - 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 and their stability in the sense of Lyapunov. - Two-dimensional diffeomorphisms such as Hénon maps and twits maps of the annulus and torus. - 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. - Teichmüller theory and connections with low dimensional dynamics and geometry. - Differentiable and continuous ergodic theory of finite and infinite measures. - Ergodic optimization. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (21)
(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)
BISSACOT, RODRIGO; GARIBALDI, EDUARDO; THIEULLEN, PHILIPPE. Zero-temperature phase diagram for double-well type potentials in the summable variation class. Ergodic Theory and Dynamical Systems, v. 38, n. 3, p. 863-885, . (11/16265-8, 15/10398-7)
ABBONDANDOLO, ALBERTO; BRAMHAM, BARNEY; HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S.. Sharp systolic inequalities for Reeb flows on the three-sphere. INVENTIONES MATHEMATICAE, v. 211, n. 2, p. 687-778, . (11/16265-8)
BISSACOT, RODRIGO; FREIRE, JR., RICARDO DOS SANTOS. On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof. Ergodic Theory and Dynamical Systems, v. 34, n. 4, p. 1103-1115, . (11/16265-8)
HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S.. Elliptic bindings for dynamically convex Reeb flows on the real projective three-space. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 55, n. 2, . (13/20065-0, 11/16265-8)
SAGHIN, RADU; VARGAS, EDSON. Invariant Measures for Cherry Flows. Communications in Mathematical Physics, v. 317, n. 1, p. 55-67, . (11/16265-8)
JAEGER, T.; TAL, F.. Irrational rotation factors for conservative torus homeomorphisms. Ergodic Theory and Dynamical Systems, v. 37, n. 5, p. 1537-1546, . (11/16265-8)
BISSACOT, RODRIGO; ENDO, ERIC OSSAMI; VAN ENTER, AERNOUT C. D.. Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields. Stochastic Processes and their Applications, v. 127, n. 12, p. 4126-4138, . (16/08518-7, 11/16265-8, 15/14434-8, 14/10637-9)
RAGAZZO, CLODOALDO GROTTA; DE BARROS VIGLIONI, HUMBERTO HENRIQUE. Hydrodynamic Vortex on Surfaces. JOURNAL OF NONLINEAR SCIENCE, v. 27, n. 5, p. 1609-1640, . (11/16265-8)
BONNOT, S.; DE CARVALHO, A.; MESSAOUDI, A.. Julia sets for Fibonacci endomorphisms of (2). DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 33, n. 4, p. 622-645, . (11/12650-4, 11/16265-8)
BISSACOT, RODRIGO; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; LE NY, ARNAUD. Entropic Repulsion and Lack of the g-Measure Property for Dyson Models. Communications in Mathematical Physics, v. 363, n. 3, p. 767-788, . (15/14434-8, 16/25053-8, 14/10637-9, 16/08518-7, 11/16265-8)
MARKARIAN, R.; ROLLA, L. T.; SIDORAVICIUS, V.; TAL, F. A.; VARES, M. E.. Stochastic perturbations of convex billiards. Nonlinearity, v. 28, n. 12, p. 4425-4434, . (11/16265-8)
HRYNIEWICZ, UMBERTO L.; LICATA, JOAN E.; SALOMAO, PEDRO A. S.. A dynamical characterization of universally tight lens spaces. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 110, n. 1, p. 213-269, . (11/16265-8)
TAL, FABIO ARMANDO. On non-contractible periodic orbits for surface homeomorphisms. Ergodic Theory and Dynamical Systems, v. 36, n. 5, p. 1644-1655, . (11/16265-8)
ALON, NOGA; BISSACOT, RODRIGO; ENDO, ERIC OSSAMI. Counting contours on trees. LETTERS IN MATHEMATICAL PHYSICS, v. 107, n. 5, p. 887-899, . (11/16265-8, 14/10637-9, 16/08518-7, 15/14434-8)
RAGAZZO, C.; RUIZ, L. S.. Viscoelastic tides: models for use in Celestial Mechanics. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 128, n. 1, p. 19-59, . (11/16265-8)
ADDAS-ZANATA, SALVADOR; SALOMAO, PEDRO A. S.. Persistence of fixed points under rigid perturbations of maps. FUNDAMENTA MATHEMATICAE, v. 227, n. 1, p. 1-19, . (11/16265-8)
HRYNIEWICZ, UMBERTO; MOMIN, AL; SALOMAO, PEDRO A. S.. A Poincare-Birkhoff theorem for tight Reeb flows on S-3. INVENTIONES MATHEMATICAE, v. 199, n. 2, p. 333-422, . (11/16265-8)
RAGAZZO, C.; RUIZ, L. S.. Dynamics of an isolated, viscoelastic, self-gravitating body. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 122, n. 4, p. 303-332, . (11/16265-8)
BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries. GEOMETRY & TOPOLOGY, v. 25, n. 1, p. 111-228, . (16/04687-9, 11/16265-8)
DE PAULO, NAIARA V.; SALOMAO, PEDRO A. S.. Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R-4. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 252, n. 1202, p. 1+, . (09/18586-6, 14/08113-1, 11/16265-8, 13/20065-0)

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