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Smooth linearization of nonautonomous dynamics under polynomial behaviour
Lucas Backes, Davor Dragicevic, Wenmeng Zhang
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linea…
A general approach to nonautonomous shadowing for nonlinear dynamics
Lucas Backes, Davor Dragičević
Given a nonautonomous and nonlinear differential equation \begin{equation}\label{DE} x'=A(t)x+f(t,x) \quad t\geq 0, \end{equation} on an arbitrary Banach space , we formulate ve…
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…