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Flows (Differentiable dynamical systems) --- Nonlinear theories. --- Stochastic integrals. --- Flows (Differentiable dynamical systems).

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This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rossler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos.The

Lyapunov exponents. --- Flows (Differentiable dynamical systems) --- Chaotic behavior in systems --- Mathematics.

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This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in Hörmander's form, by using the connection between stochastic flows and partial differential equations. The book stresses the author's view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughou

Stochastic geometry. --- Flows (Differentiable dynamical systems) --- Stochastic differential equations. --- Differentiable dynamical systems --- Differential equations --- Fokker-Planck equation --- Geometry --- Equations différentielles stochastiques --- Géométrie stochastique