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Award ID contains: 2247966

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  1. ; ; (, Letters in Mathematical Physics)
    Abstract The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals. 
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  2. ; (, Journal of Dynamics and Differential Equations)
    Abstract We prove the nonstationary bounded distortion property for$$C^{1 + \varepsilon }$$ C 1 + ε smooth dynamical systems on multidimensional spaces. The results we obtain are motivated by potential application to study of spectral properties of discrete Schrödinger operators with potentials generated by Sturmian sequences. 
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  3. (, Annales Henri Poincaré)
    We prove the nonstationary bounded distortion property for smooth dynamical systems on multidimensional spaces. The results we obtain are motivated by potential application to study of spectral properties of discrete Schrödinger operators with potentials generated by Sturmian sequences. 
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    Free, publicly-accessible full text available May 19, 2026
  4. (, Groups, Geometry, and Dynamics)
    We consider a non-stationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image, we establish a weak-* convergence to the unique invariant under isometries measure, ergodic theorem and large deviation type estimate. We also show that all the results can be carried over to the case of a random walk on a compact metrizable group. In particular, we prove a non-stationary analog of classical Itô–Kawada theorem and give a new alternative proof for the stationary case. 
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    Free, publicly-accessible full text available January 27, 2026
  5. ; (, Communications of the American Mathematical Society)
    We consider discrete Schrödinger operators on ℓ<#comment/> 2 ( Z ) \ell ^2(\mathbb {Z}) with bounded random but not necessarily identically distributed values of the potential. We prove spectral localization (with exponentially decaying eigenfunctions) as well as dynamical localization for this model. An important ingredient of the proof is a non-stationary version of the parametric Furstenberg Theorem on random matrix products, which is also of independent interest. 
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    Free, publicly-accessible full text available January 1, 2026
  6. (, Proceedings of the American Mathematical Society)
    We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate. 
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  7. ; (, Moscow Mathematical Journal)
    Ilyashenko, Yu; Tsfasman, M; Gusein-Zade, S (Ed.)
    We prove a version of pointwise ergodic theorem for non- stationary random dynamical systems. Also, we discuss two specificc examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix products. 
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