5 papers
Quasi-shadowing for partially hyperbolic dynamics on Banach spaces
Lucas Backes, Davor Dragicevic
A partially hyperbolic dynamical system is said to have the quasi-shadowing property if every pseudotrajectory can be shadowed by a sequence of points such that $…
Cohomology of fiber-bunched twisted cocycles over hyperbolic systems
Lucas Backes
A twisted cocycle taking values on a Lie Group is a cocycle that, in each step, is twisted by an automorphism of . In the case when , we prove that if tw…
On the spectral radius of compact operator cocycles
Lucas Backes, Davor Dragicevic
We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger-Wang's formula when restricted to the space of cocy…
Shadowing for nonautonomous dynamics
Lucas Backes, Davor Dragicevic
We prove that whenever a sequence of invertible and bounded operators acting on a Banach space admits an exponential dichotomy and a sequence of diffe…
A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems
Lucas Backes, Mauricio Poletti
We prove a Livšic-type theorem for Hölder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever is a non-unifo…