5 citations · 7 across the 8 of their papers we have counts for
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Variational principles for metric mean dimension with potential of level sets
Lucas Backes, Chunlin Liu, Fagner B. Rodrigues
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entr…
A characterization of -dichotomies via admissibility
Lucas Backes, Davor Dragicevic
We present a characterization of -dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spa…
Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations
Lucas Backes, Davor Dragicevic, Mihaly Pituk
It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is av…
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…