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math.DS2025
Spectral characterization of shadowing for linear operators on Hilbert spaces
Mihály Pituk
In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of…
math.DS2024★ 5 cited
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…
math.DS2024
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…