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Topology, geometry and ergodic theory of dynamical systems

Grant number: 08/02841-4
Support Opportunities:Research Projects - Thematic Grants
Duration: April 01, 2009 - March 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Jorge Manuel Sotomayor Tello
Grantee:Jorge Manuel Sotomayor Tello
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated researchers:Ali Messaoudi ; Ali Tahzibi ; Americo Lopez Galvez ; Benito Frazao Pires ; Carlos Alberto Maquera Apaza ; Daniel Smania Brandão ; Pedro Paulo de Magalhaes Rios ; Vanderlei Minori Horita
Associated scholarship(s):11/11663-5 - Ergodic and algebraic properties for dynamical systems which preserves an infinite measure, BP.PD
11/05426-0 - Noncommutative integration theory and hyperbolic dynamics, BP.MS
10/17397-2 - Dynamics of holomorphic correspondences, BP.DR
 + associated scholarships 10/17419-6 - Transversal families of piecewise expanding maps, BP.DR
10/07267-4 - Remormalization theory and thermodynamic formalism, BP.PD
09/17153-9 - Perturbations o Lorenz-like flows., BP.DR
09/13882-6 - Codimension one Anosov actions of R^k, BE.PQ - associated scholarships

Abstract

In this project, we study many aspects of the theory of dynamical systems, including: A. Perturbation of dynamical systems: Closing lemma-type problems, ergodic and stochastic stability, bifurcations in families of either discrete or continuous dynamical systems, differentiability of SBR measures, stability of the spectrum of stochastic adding machines. B. Ergodic and geometric aspects of dynamical systems: asymptotic behavior of flows on the plane with a unique singularity, existence and uniqueness of SBR measures, fractal dimension of invariant sets. C. Dynamical Systems of algebraic, geometric or semi-classic origin: Rauzy fractals, differential equations of lines of curvature and asymptotics of a surface, semiclassical dynamical systems coming from the study of non-Liouvillian propagation of semiclassical Wigner functions of pure states. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (16)
(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)
LOPES, A. O.; OLIVEIRA, E. R.; SMANIA, D.. Ergodic transport theory and piecewise analytic subactions for analytic dynamics. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 43, n. 3, p. 467-512, . (08/02841-4)
LOPES, DEBORA; SOTOMAYOR, JORGE; GARCIA, RONALDO. Umbilic singularities and lines of curvature on ellipsoids of R-4. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 45, n. 3, p. 453-483, . (08/02841-4)
SMANIA, DANIEL. Shy shadows of infinite-dimensional partially hyperbolic invariant sets. Ergodic Theory and Dynamical Systems, v. 39, n. 5, p. 1361-1400, . (10/08654-1, 03/03107-9, 08/02841-4)
BARBOT, THIERRY; MAQUERA, CARLOS. Algebraic Anosov actions of nilpotent Lie groups. Topology and its Applications, v. 160, n. 1, p. 199-219, . (08/02841-4, 09/06328-2, 09/13882-6)
DE LIMA, AMANDA; SMANIA, DANIEL. On infinitely cohomologous to zero observables. Ergodic Theory and Dynamical Systems, v. 33, n. 2, p. 375-399, . (03/03107-9, 10/17419-6, 10/08654-1, 08/02841-4)
PIRES, BENITO; TEIXEIRA, MARCO ANTONIO. On global linearization of planar involutions. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 43, n. 4, p. 637-653, . (09/02380-0, 07/06896-5, 08/02841-4)
BASTOS, J.; MESSAOUDI, A.; RODRIGUES, T.; SMANIA, D.. A class of cubic Rauzy fractals. THEORETICAL COMPUTER SCIENCE, v. 588, p. 114-130, . (13/24541-0, 08/02841-4)
SMANIA, DANIEL. Solenoidal attractors with bounded combinatorics are shy. ANNALS OF MATHEMATICS, v. 191, n. 1, p. 1-79, . (03/03107-9, 10/08654-1, 17/06463-3, 08/02841-4)
LOPES, D.; SOTOMAYOR, J.; GARCIA, R.. Partially umbilic singularities of hypersurfaces of R-4. BULLETIN DES SCIENCES MATHEMATIQUES, v. 139, n. 4, p. 431-472, . (08/02841-4)
PIRES, BENITO; RABANAL, ROLAND. VECTOR FIELDS WHOSE LINEARISATION IS HURWITZ ALMOST EVERYWHERE. Proceedings of the American Mathematical Society, v. 142, n. 9, p. 3117-3128, . (09/02380-0, 08/02841-4)
MESSAOUDI, A.; SMANIA, D.. EIGENVALUES OF FIBONACCI STOCHASTIC ADDING MACHINE. Stochastics and Dynamics, v. 10, n. 2, p. 291-313, . (08/02841-4, 03/03107-9)
BALADI, VIVIANE; SMANIA, DANIEL. LINEAR RESPONSE FOR SMOOTH DEFORMATIONS OF GENERIC NONUNIFORMLY HYPERBOLIC UNIMODAL MAPS. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, v. 45, n. 6, p. 861-926, . (08/02841-4, 10/08654-1)
CUNHA, KLEYBER; SMANIA, DANIEL. Renormalization for piecewise smooth homeomorphisms on the circle. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 30, n. 3, p. 441-462, . (07/01045-7, 08/02841-4, 10/08654-1)
NOGUEIRA, ARNALDO; PIRES, BENITO; TROUBETZKOY, SERGE. Orbit structure of interval exchange transformations with flip. Nonlinearity, v. 26, n. 2, p. 525-537, . (09/02380-0, 08/02841-4)
CUNHA, KLEYBER; SMANIA, DANIEL. Rigidity for piecewise smooth homeomorphisms on the circle. ADVANCES IN MATHEMATICS, v. 250, p. 193-226, . (08/02841-4, 10/08654-1)
BARBOT, THIERRY; MAQUERA, CARLOS. ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R-k. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 29, n. 3, p. 803-822, . (09/06328-2, 09/13882-6, 08/02841-4)

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