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Sarnak’s Conjecture for Irregular Flows on Infinite-dimensional Torus
Sarnak’s Disjointness Conjecture states that the Möbius function is disjoint with any zero-entropy flow. This note establishes this conjecture, with...
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Substitutive Systems and a Finitary Version of Cobham’s Theorem
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive....
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On Some Convergence to the Constant \(\varvec{e}\) and Proof of Keller’s Limit
A new asymptotic formula for the constant e is proposed by the continued fraction approximation. As a consequence, we deduce inequalities for the...
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Van der Corput sets with respect to compact groups
We study the notion of van der Corput sets with respect to general compact groups.
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Unipotent Flow on \( \text{SL}_2 \left( {\Bbb Z} \right)\backslash \text{SL}_2 \left( {\mathbb{R}} \right) \) : From Dynamics to Elementary Number Theory
In this paper we give a simple and elementary proof of a quantitative density result for unipotent flow on...
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Multifractal spectra and multifractal zeta-functions
We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the...
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On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions
We study the topology of a set naturally arising from the study of β -expansions. After proving several elementary results for this set we study the...
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Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle
We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle
T . A... -
Ergodic characterization of van der Corput sets
We prove an analogue to the well-known equivalence of intersective sets and Poincaré recurrent sets, in a stronger setting. We show that a set D is...
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Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure
Let { S i }
i =1 l be an iterated function system (IFS) on ℝ d with attractor K. Let π be the canonical projection. In this paper, we define a new... -
Ergodic transport theory and piecewise analytic subactions for analytic dynamics
We consider a piecewise analytic real expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and a real analytic positive...
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Equidistribution of Periodic Points for Modular Correspondences
Let T be an exterior modular correspondence on an irreducible locally symmetric space X . We show that the isolated fixed points of the power T ...
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Calculating the numbers of representations and the Garsia entropy in linear numeration systems
Given a ≥ b , let G 0 = 1, G 1 = a + 1, and G n +2 = aG n +1 + bG n for n ≥ 0. For each choice of a and b , we have a linear recurrence that defines a...
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A Decomposition of the Rotation of Circle
The paper concerns the dynamics-related properties of the rotation map of a circle (rotation of the plane). A self-similar structure of orbits of the...
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Zeta measures and Thermodynamic Formalism for temperature zero
We address the analysis of the following problem: given a real Hölder potential f defined on the Bernoulli space and μ f its equilibrium state, it is...
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Recurrence properties of sequences of integers
In order to study the recurrence of sequences of integers, we investigate their L 2 -exactness and Θ-Hartman property (Θ being a set of rational...
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Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues
Kolmogorov discovered in 1933 that the empirical statistics of several independent values of any random variable differs from the true distribution...
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Homoclinic points of non-expansive automorphisms
We study homoclinic points of non-expansive automorphisms of compact abelian groups. Connections between the existence of non-trivial homoclinic...