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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Jambaa S.
SOME CLASSICAL THEOREMS, PROPERTIES AND EXAMPLES OF ERGODIC THEORY OF DYNAMICAL SYSTEMS // BSU bulletin. Mathematics, Informatics. - 2017. №2. . - С. 3-7.
Title:
SOME CLASSICAL THEOREMS, PROPERTIES AND EXAMPLES OF ERGODIC THEORY OF DYNAMICAL SYSTEMS
Financing:
Codes:
DOI: 10.18101/2304-5728-2017-2-3-7UDK: 517.9
Annotation:
Long periods of observation of particles with the same erosion in a certain area of the phase space of microstates require the use and justification of the hypothesis that all available microstates are equiprobable. This hypothesis is equivalent to pro- visions on ergodicity in Hamiltonian systems; the ergodicity is that consecutive measurements of the states of an individual particle give the same result as meas- urements of the state of a whole system. The article discusses a number of succes- sive theorems and properties of measure-preserving transformations of dynamic systems. We have generalized some important properties of dynamical systems such as ergodicity, confusion, isomorphism, identified their relationships, improved proof of some classical theorems.
Keywords:
successive theorems and properties of measure-preserving transformations of dynamic systems.
List of references: