Stochastic Geometric Mechanics

Develops a synergistic framework of relationships among the key mathematical fields in the new science of stochastic geometric mechanics

Provides multiple pathways of communication and learning that lead from stochastic analysis to fluid dynamics, to coadjoint motion in geometric mechanics, including nonholonomic constraints and gauge theory, and to invariant probability measures for stochastic dynamics on Lie groups

Communicates key ideas in the context of simple, well-chosen examples in each of the components of stochastic geometric mechanics that were presented at the CIB program

Contenu
A. Arnaudon, A. L. De Castro and D. D. Holm , Noise and dissipation in rigid-body motion.- F. Flandoli , An open problem in the theory of regularization of noise for nonlinear PSDs.- G. Da Prato , Surface integrals in Hilbert spaces for general measures and applications.- F. Gay-Balmaz and V. Putkaradze , On noise extensions of nonholonomic constrants.- G. S. Chirikjian , Degenerate diffusions and harmonic analysis on SE(3). A tutorial.- B. Janssens and K. H. Neeb , Covariant central extensions of gauge Lie algebras.- Th. Lévy and A. Sengupta , Four chapters on Low-dimensional Gauge theories.- Y. Brenier , Some variational and stochastic methods for the Euler equations of incompressible fluid dynamics and related models.- G. A. Chechkhin , Introduction to homogenization theory.- L. Bittner, H. Gottschalk, M. Gröger, N. Moch, M. Saad, and S. Schmitz , Modeling, minimizing and managing the risk of fatigue for mechanical compo nents.- Index.