Naslov
On the exponential stability and hyperbolicity of linear cocycles

Autori
Dragičević, Davor

Izvornik
Linear and multilinear algebra (0308-1087) 69 (2021), 2; 259-277

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
linear cocycle ; exponential stability ; hyperbolicity

Sažetak
We prove that any uniformly exponentially stable linear cocycle of matrices defined over a topological dynamical system can be reduced via suitable change of variables to a linear cocycle whose generator has a spectral norm less than $1$ at each point. Moreover, we establish an analogous result for nonuniformly exponentially stable linear cocycles, i.e. cocycles with negative Lyapunov exponents. In addition, by using tools from ergodic theory, we obtain converse results that give conditions for (non)uniform exponential stability of linear cocyles under the assumption that they admit a suitable reduction to a linear cocycle whose generator has a spectral norm less than $1$ at points that form a ``large'' subset of our topological dynamical system in the appropriate sense. Finally, we discuss the versions of our results in the case of (non)uniformly hyperbolic linear cocyles.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA