Sergey Tikhomirov

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We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymp-totics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are(More)
We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyper-bolic set that is not contained in a locally maximal one. Additionally , we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov(More)
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