A realização de minicursos como meio de promover a formação de professores e a elevação da qualidade de ensino da escola-participante

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Rigidity for partially hyperbolic diffeomorphisms

In this work we completely classify (Formula presented.) conjugacy for smooth conservative (pointwise) partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism on the 3-torus by its center foliation behavior. We prove that the uniform version of absolute continuity for the center foliation is the natural hypothesis to obtain (Formula presented.) conjugacy to its linear Anosov automorphism. Avila, Viana and Wilkinson [Absolute continuity, Lyapunov exponents and rigidity I: Geodesic flows. J. Eur. Math. Soc. (JEMS) 17(6) (2015), 1435–1462] proved that for a perturbation in the volume preserving case of the time-one map of an Anosov flow absolute continuity of the center foliation implies smooth rigidity. The absolute version of absolute continuity is the appropriate scenario for our context since it is not possible to obtain a result analogous to that of Avila, Viana and Wilkinson for our class of maps, for absolute continuity alone fails miserably to imply smooth rigidity for our class of maps. Our theorem is a global rigidity result as we do not assume the diffeomorphism to be at some distance from the linear Anosov automorphism. We also do not assume ergodicity. In particular, a metric condition on the center foliation implies ergodicity and (Formula presented.) center foliation. © Cambridge University Press, 20173883188320

Lyapunov exponents and smooth invariant foliations for partially hyperbolic diffeomorphisms on

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOThis paper is concerned with the rigidity problem for volume preserving partially hyperbolic diffeomorphisms on [GRAPHICS] homotopic to a linear Anosov on [GRAPHICS] . We characterize the C1+theta conjugacy of such diffeomorphisms in terms of smooth conditions on the stable and unstable foliations. The smooth conditions on the foliations are to be C-1 foliations and transversely absolutely continuous with bounded Jacobians. In particular these conditions for only one direction (stable, centre or unstable) completely determine the Lyapunov exponents.This paper is concerned with the rigidity problem for volume preserving partially hyperbolic diffeomorphisms on [GRAPHICS] homotopic to a linear Anosov on [GRAPHICS] . We characterize the C1+theta conjugacy of such diffeomorphisms in terms of smooth conditions on the stable and unstable foliations. The smooth conditions on the foliations are to be C-1 foliations and transversely absolutely continuous with bounded Jacobians. In particular these conditions for only one direction (stable, centre or unstable) completely determine the Lyapunov exponents.302189199FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP [2011/21214-3, 2012/06553-9]2011/21214-3, 2012/06553-

Maintaining Translational Relevance in Animal Models of Manganese Neurotoxicity

Manganese is an essential metal, but elevated brain Mn concentrations produce a parkinsonian-like movement disorder in adults and fine motor, attentional, cognitive, and intellectual deficits in children. Human Mn neurotoxicity occurs owing to elevated exposure from occupational or environmental sources, defective excretion (e.g., due to cirrhosis), or loss-of-function mutations in the Mn transporters solute carrier family 30 member 10 or solute carrier family 39 member 14. Animal models are essential to study Mn neurotoxicity, but in order to be translationally relevant, such models should utilize environmentally relevant Mn exposure regimens that reproduce changes in brain Mn concentrations and neurological function evident in human patients. Here, we provide guidelines for Mn exposure in mice, rats, nematodes, and zebrafish so that brain Mn concentrations and neurobehavioral sequelae remain directly relatable to the human phenotype