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Topology, geometry and ergodic theory of dynamical systems

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)

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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, 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, . (09/13882-6, 09/06328-2, 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)
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)
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)
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)
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)
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)
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, . (08/02841-4, 09/02380-0)
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)
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, . (08/02841-4, 07/01045-7, 10/08654-1)
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)
NOGUEIRA, ARNALDO; PIRES, BENITO; TROUBETZKOY, SERGE. Orbit structure of interval exchange transformations with flip. Nonlinearity, v. 26, n. 2, p. 525-537, . (08/02841-4, 09/02380-0)
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.