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One admissible critical pair without Lyapunov norm implies a tempered exponential dichotomy for Met-systems.
- Source :
-
Stochastics & Dynamics . Nov2023, Vol. 23 Issue 7, p1-22. 22p. - Publication Year :
- 2023
-
Abstract
- It is known that a tempered exponential dichotomy (which is the version of nonuniform exponential dichotomy for random dynamical systems) can be described by admissibility of a pair of function classes defined in terms of Lyapunov norms. Moreover, for MET-systems (i.e. random dynamical systems which satisfy the assumptions of the Multiplicative Ergodic Theorem) over an ergodic base system, tempered exponential dichotomy can be described by admissibility of a pair of function spaces which are defined in terms of the original norm. In present paper, we find an admissibility description of tempered exponential dichotomies for MET-systems in terms of new output and input classes. These classes can be regarded as a critical case of admissibility classes in the known result. Finally, we use our new pair of admissible spaces to prove the roughness of tempered exponential dichotomies for parametric MET-systems and give a Hölder continuous dependence of the associated projections on the parameter. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EXPONENTIAL dichotomy
*RANDOM dynamical systems
*HOLDER spaces
*FUNCTION spaces
Subjects
Details
- Language :
- English
- ISSN :
- 02194937
- Volume :
- 23
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Stochastics & Dynamics
- Publication Type :
- Academic Journal
- Accession number :
- 175504153
- Full Text :
- https://doi.org/10.1142/S0219493723500533