Minimal invariant closed sets of set-valued semiflows
- Resource Type
- Authors
- Grzegorz Guzik
- Source
- Journal of Mathematical Analysis and Applications. 449:382-396
- Subject
- Discrete mathematics
Mathematics::Dynamical Systems
Closed set
Stochastic process
Applied Mathematics
010102 general mathematics
Mathematics::Classical Analysis and ODEs
Mathematics::Analysis of PDEs
01 natural sciences
Random dynamical systems
010101 applied mathematics
Metric space
Bounded function
Ergodic theory
Invariant measure
0101 mathematics
Invariant (mathematics)
Analysis
Mathematics
- Language
- ISSN
- 0022-247X
In the paper we deal with minimal closed subsets invariant with respect to set-valued semiflow. Such sets are known as supports of invariant or even ergodic measures of stochastic processes associated with such semiflows. Our motivation comes from some earlier and recent results connected with bounded noise processes, but we work in the framework of set-valued semiflows with lower semicontinuous members on general metric space rather than mostly studied by many authors continuous and compact-valued ones. Such semiflows appear naturally when nonautonomous/random dynamical systems are considered.