Low dimensional dynamics

• Grant number: 11/16265-8
• Support Opportunities: Research Projects - Thematic Grants
• Start date: April 01, 2012
• End date: 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
• City of the host institution: São Paulo
• Principal investigators: Albert Meads Fisher ; Clodoaldo Grotta Ragazzo ; Edson de Faria ; Fábio Armando Tal ; Pedro Antonio Santoro Salomão ; Salvador Addas Zanata
• Principal investigators: Edson Vargas
• Associated researchers: Eduardo Colli ; MANUEL VALENTIM DE PERA GARCIA ; Ricardo dos Santos Freire Júnior ; Rodrigo Bissacot Proença
• Associated research 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

(27)

(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, MAY 2018. (11/16265-8, 15/10398-7)

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. (11/16265-8)

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. (11/16265-8)

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. (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, APR 2016. (13/20065-0, 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, p. 57-pg., 2015-01-01. (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, AUG 2017. (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, AUG 2016. (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, JAN 2015. (11/16265-8)

SAGHIN, RADU; VARGAS, EDSON. Invariant Measures for Cherry Flows. Communications in Mathematical Physics, v. 317, n. 1, p. 55-67, JAN 2013. (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, 2014. (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+, MAR 2018. (09/18586-6, 14/08113-1, 11/16265-8, 13/20065-0)

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. (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, DEC 2015. (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, FEB 2015. (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, MAY 2017. (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, MAY 2017. (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, DEC 2017. (16/08518-7, 11/16265-8, 15/14434-8, 14/10637-9)

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. (15/14434-8, 16/25053-8, 14/10637-9, 16/08518-7, 11/16265-8)

JAEGER, T.; TAL, F.. Irrational rotation factors for conservative torus homeomorphisms. Ergodic Theory and Dynamical Systems, v. 37, p. 10-pg., 2017-08-01. (11/16265-8)

BISSACOT, RODRIGO; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; KIMURA, BRUNO; LE NY, ARNAUD; RUSZEL, WIOLETTA M.; SIDORAVICIUS, V. Dyson Models Under Renormalization and in Weak Fields. SOJOURNS IN PROBABILITY THEORY AND STATISTICAL PHYSICS - I: SPIN GLASSES AND STATISTICAL MECHANICS, A FESTSCHRIFT FOR CHARLES M. NEWMAN, v. 298, p. 15-pg., 2019-01-01. (14/10637-9, 11/16265-8, 15/14434-8)

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, p. 23-pg., 2018-05-01. (11/16265-8, 15/10398-7)

TAL, FABIO ARMANDO. On non-contractible periodic orbits for surface homeomorphisms. Ergodic Theory and Dynamical Systems, v. 36, p. 12-pg., 2016-08-01. (11/16265-8)

BISSACOT, RODRIGO; FREIRE, RICARDO DOS SANTOS, JR.. On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof. Ergodic Theory and Dynamical Systems, v. 34, p. 13-pg., 2014-08-01. (11/16265-8)

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. (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, 2021. (16/04687-9, 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, 2018. (11/12650-4, 11/16265-8)