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math.DS2025
Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold.…
math.DS2022
On the norm equivalence of Lyapunov exponents for regularizing linear evolution equations
Alex Blumenthal, Sam Punshon-Smith
We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differenti…
math.DS2017
The Selgrade decomposition for linear semiflows on Banach spaces
Alex Blumenthal, Yuri Latushkin
We extend Selgrade's Theorem, Morse spectrum, and related concepts to the setting of linear skew product semiflows on a separable Banach bundle. We recover a characterization, well…