3 papers
math.FA2026
Resolving the generalized hyperbolicity conjecture for shadowing
Mihály Pituk
It is known that generalized hyperbolicity implies the shadowing property for invertible bounded linear operators on a Banach space. Whether the converse holds has been a central o…
math.DS2026
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
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…