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Applications of Lie groups to differential equations Peter J. Olver
Publisher: Springer-Verlag

Within this section general relativity is briefly discussed as is Noether's theorem. Topics include: Lie groups & Lie algebras, differential geometry (vector fields, Riemannian metrics, covariant derivatives, geodesics, Killing vector fields), Lie groups and differential equations and the calculus of variations. Pistorius, Imperial College: Maximum increments of random walks and M. The book contains exercises and plenty of worked examples. Roeckner, Bielefeld: Self-organized criticality via stochastic partial differential equations. Chafai, Toulouse: Spectral analysis of large random Markov chains D. Here differential geometry is developed. Applebaum, Sheffield: Spectral properties of semigroups of measures on Lie groups. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Krasovsky, Brunel and Imperial college: Toeplitz determinants and their applications. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. Section VIII covers Lie groups and their applications. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required.