zbMATH — the first resource for mathematics

Invariant measures of smooth dynamical systems, generalized functions and summation methods. (English. Russian original) Zbl 1417.37088
Izv. Math. 80, No. 2, 342-358 (2016); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 2, 63-80 (2016).
The author discusses conditions for the existence and the regularity of invariant measures of smooth dynamical systems on compact manifolds. The author also provided examples where the invariant measures have different kinds of regularities. A new proof of the classical Bogolyubov-Krylov theorem is given using Hahn-Banach theorem.

37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C10 Dynamics induced by flows and semiflows
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
Full Text: DOI