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Low dimensional dynamics

Grant number: 11/16265-8
Support type: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
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Co-Principal Investigators:Albert Meads Fisher ; Clodoaldo Grotta Ragazzo ; Edson de Faria ; Edson Vargas ; Fábio Armando Tal ; Pedro Antonio Santoro Salomão ; Salvador Addas Zanata
Assoc. 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

Abstract

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)

Scientific publications (20)
(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)
FREIRE, RICARDO; VARGAS, VICTOR. EQUILIBRIUM STATES AND ZERO TEMPERATURE LIMIT ON TOPOLOGICALLY TRANSITIVE COUNTABLE MARKOV SHIFTS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 370, n. 12, p. 8451-8465, DEC 2018. Web of Science Citations: 2.
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, NOV 2018. Web of Science Citations: 1.
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, MAY 2018. Web of Science Citations: 5.
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+, MAR 2018. Web of Science Citations: 0.
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, FEB 2018. Web of Science Citations: 3.
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, 2018. Web of Science Citations: 1.
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, DEC 2017. Web of Science Citations: 5.
RAGAZZO, CLODOALDO GROTTA; DE BARROS VIGLIONI, HUMBERTO HENRIQUE. Hydrodynamic Vortex on Surfaces. JOURNAL OF NONLINEAR SCIENCE, v. 27, n. 5, p. 1609-1640, OCT 2017. Web of Science Citations: 3.
JAEGER, T.; TAL, F. Irrational rotation factors for conservative torus homeomorphisms. Ergodic Theory and Dynamical Systems, v. 37, n. 5, p. 1537-1546, AUG 2017. Web of Science Citations: 2.
ALON, NOGA; BISSACOT, RODRIGO; ENDO, ERIC OSSAMI. Counting contours on trees. LETTERS IN MATHEMATICAL PHYSICS, v. 107, n. 5, p. 887-899, MAY 2017. Web of Science Citations: 1.
RAGAZZO, C.; RUIZ, L. S. Viscoelastic tides: models for use in Celestial Mechanics. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 128, n. 1, p. 19-59, MAY 2017. Web of Science Citations: 3.
TAL, FABIO ARMANDO. On non-contractible periodic orbits for surface homeomorphisms. Ergodic Theory and Dynamical Systems, v. 36, n. 5, p. 1644-1655, AUG 2016. Web of Science Citations: 3.
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 APR 2016. Web of Science Citations: 1.
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, DEC 2015. Web of Science Citations: 1.
RAGAZZO, C.; RUIZ, L. S. Dynamics of an isolated, viscoelastic, self-gravitating body. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 122, n. 4, p. 303-332, AUG 2015. Web of Science Citations: 4.
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, FEB 2015. Web of Science Citations: 12.
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, JAN 2015. Web of Science Citations: 5.
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, AUG 2014. Web of Science Citations: 3.
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, 2014. Web of Science Citations: 0.
SAGHIN, RADU; VARGAS, EDSON. Invariant Measures for Cherry Flows. Communications in Mathematical Physics, v. 317, n. 1, p. 55-67, JAN 2013. Web of Science Citations: 7.

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