Publications (35)
Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems
Lucas Backes, Fagner B. Rodrigues
We introduce four, a priori different, notions of topological pressure for possibly discontinuous semiflows acting on compact metric spaces and observe that they all agree with the…
Parameterized shadowing for nonautonomous dynamics
Lucas Backes, Davor DragiÄeviÄ, Xiao Tang
For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit , shadowi…
Conditional Lipschitz shadowing for ordinary differential equations
Lucas Backes, Davor Dragicevic, Masakazu Onitsuka +1
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish t…
A general approach to nonautonomous shadowing for nonlinear dynamics
Lucas Backes, Davor DragiÄeviÄ
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…
Shadowing and hyperbolicity for linear delay difference equations
Lucas Backes, Davor Dragicevic, Mihaly Pituk
It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this paper, we prove the converse and hence the equivalence between hyperbolicity…
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 $…