Integrated methods for investigation of problems of mathematical physics, traditionally considered as far from each other, such as classical mechanics, quantum and statistical physics and hydrodynamics, are developed. Unification of these branches is based on considering the geometrically invariant form of Newton's second law or its natural generalizations (stochastic, infinite-dimensional, etc.) as the principal equation of motion. Topological characteristics of Lefschetz and Nielsen numbers type are constructed for a broad class of maps of infinite-dimensional manifolds (locally compact, weakly compact, condensing maps of Finsler manifolds, etc.).
Main publications:
Gliklikh Yu. E. Ordinary and stochastic differential geometry as a tool for mathematical physics. Dordrecht: Kluwer Academic Publishers, 1996. 205 p.
Gliklikh Yu. E. Global Analysis in Mathematical Physics. Geometric and Stochastic Methods. New York: Springer-Verlag, 1997. 229 p.
Gliklikh Yu. E. Globalnyi i stokhasticheskii analiz v zadachakh matematicheskoi fiziki. M.: KomKniga, 2005. 416 s.
Gliklikh Yu.E. Global and Stochastic Analysis with Applications to Mathematical Physics. London: Springer-Verlag, 2011. 460 p.
