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)

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)

SMANIA, DANIEL. Shy shadows of infinite-dimensional partially hyperbolic invariant sets. Ergodic Theory and Dynamical Systems, v. 39, n. 5, p. 1361-1400, MAY 2019. (10/08654-1, 03/03107-9, 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, SEP 2014. (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, JAN 1 2013. (08/02841-4, 09/06328-2, 09/13882-6)

PIRES, BENITO; TEIXEIRA, MARCO ANTONIO. On global linearization of planar involutions. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 43, n. 4, p. 637-653, DEC 2012. (09/02380-0, 07/06896-5, 08/02841-4)

DE LIMA, AMANDA; SMANIA, DANIEL. On infinitely cohomologous to zero observables. Ergodic Theory and Dynamical Systems, v. 33, n. 2, p. 375-399, APR 2013. (03/03107-9, 10/17419-6, 10/08654-1, 08/02841-4)

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, SEP 2012. (08/02841-4)

PESSOA, CLAUDIO; SOTOMAYOR, JORGE. STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS. Electronic Journal of Differential Equations, v. N/A, p. 15-pg., 2012-09-22. (08/02841-4, 11/13152-8)

DE LIMA, AMANDA; SMANIA, DANIEL. On infinitely cohomologous to zero observables. Ergodic Theory and Dynamical Systems, v. 33, p. 25-pg., 2013-04-01. (10/17419-6, 10/08654-1, 03/03107-9, 08/02841-4)

GARCIA, R.; SOTOMAYOR, J.; SPINDOLA, F.. AXIUMBILIC SINGULAR POINTS ON SURFACES IMMERSED IN R-4 AND THEIR GENERIC BIFURCATIONS. JOURNAL OF SINGULARITIES, v. 10, p. 23-pg., 2014-01-01. (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, JUL 11 2015. (13/24541-0, 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, JUN 2015. (08/02841-4)

SMANIA, DANIEL. Shy shadows of infinite-dimensional partially hyperbolic invariant sets. Ergodic Theory and Dynamical Systems, v. 39, p. 40-pg., 2019-05-01. (03/03107-9, 08/02841-4, 10/08654-1)

SMANIA, DANIEL. Solenoidal attractors with bounded combinatorics are shy. ANNALS OF MATHEMATICS, v. 191, n. 1, p. 1-79, JAN 2020. (03/03107-9, 10/08654-1, 17/06463-3, 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, SEP 2014. (09/02380-0, 08/02841-4)

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, NOV-DEC 2012. (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, MAY-JUN 2013. (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, FEB 2013. (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, JAN 15 2014. (08/02841-4, 10/08654-1)

MESSAOUDI, A.; SMANIA, D.. EIGENVALUES OF FIBONACCI STOCHASTIC ADDING MACHINE. Stochastics and Dynamics, v. 10, n. 2, p. 291-313, JUN 2010. (08/02841-4, 03/03107-9)

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, MAR 10 2011. (09/06328-2, 09/13882-6, 08/02841-4)