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Дисертації з теми "Champs différentiables"
Smail, Abderrahmane. "Propriétés qualitatives des champs de contact de Morse-Smale sur une surface." Lyon 1, 1985. http://www.theses.fr/1985LYO11664.
Повний текст джерелаStefani, Davide. "Representations up to homotopy and perfect complexes over differentiable stacks." Electronic Thesis or Diss., Sorbonne université, 2019. http://www.theses.fr/2019SORUS687.
Повний текст джерелаThis thesis is concerned with the geometry of stacks in the differential geometry context using homotopical and higher categorical techniques. These techniques becomes necessary to deal with simple stack generalizations of crucial objects such as tangent and cotangent bundles, forms on a stack, their automorphisms and more generally perfect complexes, which are one of the main object of study of this work. In the first part of this thesis we give an overview of higher and differentiable stacks, their homotopy theory and cohomology theories. In the second part we study one representation up to homotopy of Lie groupoids and rely them with a theory of perfect complex over differentiable stacks. Among our results, we show that a representation up to homotopy on a Lie groupoid is the same as a cohesive module on its dg-algebra of smooth functions and that the correspondent dg-categories are Morita invariant. This allows us to give a definition of dg-category of perfect complexes on a differentiable stack. We moreover construct a Lie 2-groupoid of automorphisms of 2-terms complexes of vector bundles, which is a higher analogue of the classifying stack BGL_n. We conclude by giving a definition of the differentiable 2-stack of perfect complexes of amplitude [0,1] by means of a Lie 2-groupoid presenting it
Lee, Huaiqian. "Flots quasi-invariants associés aux champs de vecteur non réguliers." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS100/document.
Повний текст джерелаThe thesis mainly consists of two parts.In the first part, we study the quasi-invariant flow generated by the Stratonovich stochas-tic differential equation with BV drift coefficients in the Euclidean space. We generalizethe results of Ambrosio [Invent. Math. 158 (2004), 227{260] on the existence, uniquenessand stability of regular Lagrangian flows of ordinary differential equations to Stratonovichstochastic differential equations with BV drift coefficients. As an application of the sta-bility result, we construct an explicit solution to the corresponding stochastic transportequation in terms of the stochastic flow. The approximate differentiability of the flow isalso studied when the drift coefficient has some Sobolev regularity.In the second part, we generalize the DiPerna-Lions theory in the Euclidean space to thecomplete Riemannian manifold. We define the commutator on the complete Riemannianmanifold which is a probabilistic version of the one in the DiPerna-Lions theory, andestablish the commutator estimate by the probabilistic method. As a direct applicationof the commutator estimate, we investigate the uniqueness of solutions to the transportequation by the method of the renormalized solution. Following Ambrosio's method, weconstruct the DiPerna-Lions flow on the Riemannian manifold. In order to construct thediffusion process associated to an elliptic operator with irregular drift on the completeRiemannian manifold, we give some conditions which guarantee the strong completenessof the horizontal flow. Finally, we construct the diffusion process with the drift coefficienthaving only Sobolev regularity.Besides, we present a brief introduction of the classical theory on the ordinary differentialequation in the smooth case and the quasi-invariant flow of homeomorphisms under theOsgood condition before the first part; and we recall some basic tools and results whichare widely used throughout the whole thesis after the second part
Chotard, Alexandre. "Markov chain Analysis of Evolution Strategies." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112230/document.
Повний текст джерелаIn this dissertation an analysis of Evolution Strategies (ESs) using the theory of Markov chains is conducted. Proofs of divergence or convergence of these algorithms are obtained, and tools to achieve such proofs are developed.ESs are so called "black-box" stochastic optimization algorithms, i.e. information on the function to be optimized are limited to the values it associates to points. In particular, gradients are unavailable. Proofs of convergence or divergence of these algorithms can be obtained through the analysis of Markov chains underlying these algorithms. The proofs of log-linear convergence and of divergence obtained in this thesis in the context of a linear function with or without constraint are essential components for the proofs of convergence of ESs on wide classes of functions.This dissertation first gives an introduction to Markov chain theory, then a state of the art on ESs and on black-box continuous optimization, and present already established links between ESs and Markov chains.The contributions of this thesis are then presented:o General mathematical tools that can be applied to a wider range of problems are developed. These tools allow to easily prove specific Markov chain properties (irreducibility, aperiodicity and the fact that compact sets are small sets for the Markov chain) on the Markov chains studied. Obtaining these properties without these tools is a ad hoc, tedious and technical process, that can be of very high difficulty.o Then different ESs are analyzed on different problems. We study a (1,\lambda)-ES using cumulative step-size adaptation on a linear function and prove the log-linear divergence of the step-size; we also study the variation of the logarithm of the step-size, from which we establish a necessary condition for the stability of the algorithm with respect to the dimension of the search space. Then we study an ES with constant step-size and with cumulative step-size adaptation on a linear function with a linear constraint, using resampling to handle unfeasible solutions. We prove that with constant step-size the algorithm diverges, while with cumulative step-size adaptation, depending on parameters of the problem and of the ES, the algorithm converges or diverges log-linearly. We then investigate the dependence of the convergence or divergence rate of the algorithm with parameters of the problem and of the ES. Finally we study an ES with a sampling distribution that can be non-Gaussian and with constant step-size on a linear function with a linear constraint. We give sufficient conditions on the sampling distribution for the algorithm to diverge. We also show that different covariance matrices for the sampling distribution correspond to a change of norm of the search space, and that this implies that adapting the covariance matrix of the sampling distribution may allow an ES with cumulative step-size adaptation to successfully diverge on a linear function with any linear constraint.Finally, these results are summed-up, discussed, and perspectives for future work are explored
Книги з теми "Champs différentiables"
Curtis, W. D. Differential manifolds and theoretical physics. Orlando [Fla.]: Academic Press, 1985.
Знайти повний текст джерелаCurtis, W. D. Differential manifolds and theoretical physics. Orlando [Fla.]: Academic Press, 1985.
Знайти повний текст джерелаElementary symbolic dynamics and chaos in dissipative systems. Singapore: World Scientific, 1989.
Знайти повний текст джерелаDiscrete chaos: With applications in science and engineering. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2008.
Знайти повний текст джерелаDiscrete chaos. Boca Raton, Fla: Chapman & Hall/CRC, 2000.
Знайти повний текст джерелаAn introduction to chaotic dynamical systems. 2nd ed. Redwood City, Calif: Addison-Wesley, 1989.
Знайти повний текст джерелаAn introduction to chaotic dynamical systems. 2nd ed. Boulder, Colo: Westview Press, 2003.
Знайти повний текст джерелаAn introduction to chaotic dynamical systems. Menlo Park, Calif: Benjamin/Cummings, 1986.
Знайти повний текст джерелаIntroduction to chaos and coherence. Bristol: Institute of Physics Publishing, 1992.
Знайти повний текст джерелаDiscrete dynamical systems: Theory and applications. Oxford [England]: Clarendon Press, 1990.
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