Related papers: Almost Countable Spectrum and Logarithmic Sarnak C…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite…
For numerical sequences taking values $0$ or complex numbers of modulus $1$, we define Chowla property and Sarnak property. We prove that Chowla property implies Sarnak property. We also prove that for Lebesgue almost every $\beta>1$, the…
The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability…
We prove that among the set of smooth diffeomorphisms there exists a $C^1$-open and dense subset of data such that either the Lagrange spectrum is finite and the dynamics is a Morse-Smale diffeomorphism or the Lagrange spectrum has positive…
In many dynamical systems, countably infinitely many invariant tori co-exist. The occurrence of quasiperiodicity on any one of these tori is sometimes sufficient to establish strong global properties, like dense trajectories and periodic…
Discrete time random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniform continuous and contractive are considered. A notion of a…
We explore the notion of discrete spectrum and its various characterizations for ergodic measure-preserving actions of an amenable group on a compact metric space. We introduce a notion of 'weak-tameness', which is a measure-theoretic…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
We show that a minimal toplogical dynamical system that is frequently stable if and only if it is almost automorphic.
Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product $C^*$-algebras is discussed. For the Cantor minimal systems, a complete…
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…
Downarowicz and Maass (2008) proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this definition to the case of all essentially minimal…
We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set…
This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral gaps of the almost Mathieu operator, addressing a question…
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…
We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…
Motivated by the variations of Sarnak's conjecture due to El Abdalaoui, Kulaga-Przymus, Lemanczyk, De La Rue and by the observation that the Mobius function is a good weight (with limit zero) for the polynomial pointwise ergodic theorem in…
Almost finiteness was introduced in the seminal work of Kerr as an dynamical analogue of Z-stability in the Toms-Winter conjecture. In this article, we provide the first examples of minimal, topologically free actions of amenable groups…
For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the…