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Dynamics and geometry in low dimensions

Grant number: 16/25053-8
Support type:Research Projects - Thematic Grants
Duration: August 01, 2017 - July 31, 2022
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 ; Clodoaldo Grotta Ragazzo ; Edson de Faria ; Edson Vargas ; Fábio Armando Tal ; Pedro Antonio Santoro Salomão ; Rodrigo Bissacot Proença ; Salvador Addas Zanata
Assoc. researchers:Fábio Armando Tal ; Luciana Luna Anna Lomonaco ; Ricardo dos Santos Freire Júnior ; Sylvain Philippe Pierre Bonnot
Associated grant(s):19/16278-4 - Exploring universality in 1-D systems, AP.R SPRINT
18/06267-2 - Invariant measures in weakly hyperbolic dynamics, AV.EXT
17/26645-9 - Thermodynamic formalism and KMS states on Countable Markov shifts, AV.BR
17/50139-6 - Rigidity in mildly smooth 1-D systems, AP.R SPRINT
17/13160-7 - Continuity of entropy and classification of partially hyperbolic systems with one-dimensional central bundle, AV.EXT
Associated scholarship(s):19/25356-9 - Stratified rheological models for icy worlds with liquid layers, BP.PD
20/07644-4 - Hyperbolic geometry in low dimensions, BP.IC
19/26825-2 - Dynamical localization on unidimensional Schrödinger operators, BP.IC
+ associated scholarships 19/26838-7 - An introduction to ergodic theory via hiperbolic groups I, BP.IC
19/26843-0 - An introduction to ergodic theory via hyperbolic groups II, BP.IC
19/26947-0 - An introduction to chaotic systems via linear dynamics, BP.IC
19/14780-4 - Annulus diffeomorphisms dynamics, BP.MS
19/15373-3 - Introduction to dynamical systems and ergodic theory, BP.IC
18/21340-8 - Geometric conditions for rigidity of Anosov actions, BP.PD
18/26698-8 - Potts models with inhomogeneous external fields, BP.DD
18/21067-0 - A probabilistic approach to spin systems, BP.DR
18/17585-5 - Topological structure of Lozi attractors, BP.PD
18/12482-3 - 1. K-theory and group actions on shift dynamical systems 2. Classification of shift spaces of finite types possessing the infinite dihedral groups, BP.PD
18/15750-9 - Closed curves on hyperbolic manifolds., BP.PD
18/13688-4 - On stretch-factors of pseudo-Anosov homeomorphisms., BP.PD
18/15088-4 - Limit theorems in dynamical systems, BP.PD
18/12483-0 - Dynamics and geometry in low dimensions, BP.PD
18/18331-7 - Dynamics and Hamiltonian systems, BP.IC
18/07797-5 - Moduli of continuity of the Lyapunov exponents for linear cocycles with holonomies, BP.PD
18/03762-2 - Topological dynamical system on surfaces, BP.PD
17/26620-6 - Systolic inequalities for Reeb flows in dimension 3, BE.PQ
17/21527-8 - Dynamics of billiards and ergodicity, BP.IC
17/18152-2 - Phase transitions on Quantum Ising Models, BP.DD
15/26253-8 - Tidal effects on the dynamics of two- and three-body systems under gravitational forces, BP.DR - associated scholarships

Abstract

This project is a continuation of two previous thematic projects supported by FAPESP with numbers 2006/03829-2 and 2011/16265-8. The present group includes researchers working on dynamical systems and low-dimensional geometry and has senior as well as and young researchers, including recent hires. The areas covered by the project are: dynamics in dimension 2: dynamics of homeomorphisms and diffeomorphisms of the torus; topological dynamics on surfaces; Hénon maps; Teichmüller Theory and its connections with dynamics and geometry in low dimensions; endomorphisms of the interval, critical circle maps, renormalization and parameter space; hamiltonian dynamics; pseudo-holomorphic curves and symplectic dynamics; complex dynamics in dimensions 1 and 2; continuous and differentiable ergodic theory of finite and infinite measures; thermodynamic formalism and ergodic optimization. The purpose of this proposal is to continue to the work we have been doing and also aims to expand the activities of the group that has grown and includes new researchers and new areas of research. (AU)

Scientific publications (10)
(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)
GEVORGYAN, YEVA; BOUE, GWENAEL; RAGAZZO, CLODOALDO; RUIZ, LUCAS S.; CORREIA, ALEXANDRE C. M. Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration. ICARUS, v. 343, JUN 2020. Web of Science Citations: 0.
BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. STATISTICAL STABILITY FOR BARGE-MARTIN ATTRACTORS DERIVED FROM TENT MAPS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 40, n. 5, p. 2903-2915, MAY 2020. Web of Science Citations: 0.
RAGAZZO, CLODOALDO. The theory of figures of Clairaut with focus on the gravitational modulus: inequalities and an improvement in the Darwin-Radau equation. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, JAN 2020. Web of Science Citations: 0.
DE PAULO, NAIARA V.; SALOMAO, PEDRO A. S. ON THE MULTIPLICITY OF PERIODIC ORBITS AND HOMOCLINICS NEAR CRITICAL ENERGY LEVELS OF HAMILTONIAN SYSTEMS IN R-4. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 372, n. 2, p. 859-887, JUL 15 2019. Web of Science Citations: 0.
ABBONDANDOLO, ALBERTO; BRAMHAM, BARNEY; HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S. Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere. COMPOSITIO MATHEMATICA, v. 154, n. 12, p. 2643-2680, DEC 2018. Web of Science Citations: 0.
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; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; KIMURA, BRUNO; RUSZEL, WIOLETTA M. Contour Methods for Long-Range Ising Models: Weakening Nearest-Neighbor Interactions and Adding Decaying Fields. ANNALES HENRI POINCARE, v. 19, n. 8, p. 2557-2574, AUG 2018. Web of Science Citations: 1.
CORREIA, A. C. M.; RAGAZZO, C.; RUIZ, L. S. The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, v. 130, n. 8 AUG 2018. Web of Science Citations: 1.
ESTEVEZ, GABRIELA; DE FARIA, EDSON; GUARINO, PABLO. Beau bounds for multicritical circle maps. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 29, n. 3, p. 842-859, JUN 2018. Web of Science Citations: 1.
GROTTA RAGAZZO, C. The motion of a vortex on a closed surface of constant negative curvature. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SC, v. 473, n. 2206 OCT 1 2017. Web of Science Citations: 2.

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