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math.DS2025
Generalized hyperbolicity for diffeomorphisms of Banach spaces
Sergey Tikhomirov
We introduce generalized hyperbolicity for nonlinear dynamics in Banach spaces. The definition allows the stable/unstable splitting to be discontinuous and requires only inclusions…
math.DS2024
Probabilistic shadowing in linear skew products
Grigorii Monakov, Sergey Tikhomirov
We investigate the probability of shadowing of a random finite pseudotrajectory by an exact trajectory for linear skew products. We describe general conditions under which a random…