Add to ORKGsummary:We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots $, where $\alpha >1$ is a Pisot number and $\xi \in {\mathbb Q}(\alpha )$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $\xi =1$ and the unique limit point is zero, was earlier described by the author and Luca, independently
AbstractLet F(z)∈R[z] be a polynomial with positive leading coefficient, and let α>1 be an algebraic...
AbstractLet S denote the set of Pisot numbers. This paper investigates the question of determining e...
In this article, we are dealing with -numeration, which is a generalization of numeration in a non-i...
Abstract. We consider the sequence of fractional parts {ξαn}, n = 1, 2, 3,..., where α> 1 is a Pi...
summary:We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots...
summary:We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
Abstract. Suppose that α> 1 is an algebraic number and ξ> 0 is a real number. We prove that th...
AbstractA Pisot number θ is said to be simple if the beta-expansion of its fractional part, in base ...
AbstractLet S denote the set of Pisot numbers. This paper investigates the question of determining e...
Thue–Morse sequence has several extremal properties among all non-periodic sequences of the symbols ...
Abstract. Given a number β>1, the beta-transformation T = Tβ is defined for x ∈ [0,1] by Tx: = βx...
AbstractIt is known that the sequence 1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,… of lengths of blocks of id...
AbstractLet F(z)∈R[z] be a polynomial with positive leading coefficient, and let α>1 be an algebraic...
AbstractLet S denote the set of Pisot numbers. This paper investigates the question of determining e...
In this article, we are dealing with -numeration, which is a generalization of numeration in a non-i...
Abstract. We consider the sequence of fractional parts {ξαn}, n = 1, 2, 3,..., where α> 1 is a Pi...
summary:We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots...
summary:We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
summary:Let $L(\theta ,\lambda )$ be the set of limit points of the fractional parts $\lbrace \lambd...
Abstract. Suppose that α> 1 is an algebraic number and ξ> 0 is a real number. We prove that th...
AbstractA Pisot number θ is said to be simple if the beta-expansion of its fractional part, in base ...
AbstractLet S denote the set of Pisot numbers. This paper investigates the question of determining e...
Thue–Morse sequence has several extremal properties among all non-periodic sequences of the symbols ...
Abstract. Given a number β>1, the beta-transformation T = Tβ is defined for x ∈ [0,1] by Tx: = βx...
AbstractIt is known that the sequence 1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,… of lengths of blocks of id...
AbstractLet F(z)∈R[z] be a polynomial with positive leading coefficient, and let α>1 be an algebraic...
AbstractLet S denote the set of Pisot numbers. This paper investigates the question of determining e...
In this article, we are dealing with -numeration, which is a generalization of numeration in a non-i...