Zobrazeno 1 - 10
of 152
pro vyhledávání: '"Dajani, Karma"'
Autor:
Dajani, Karma, Huang, Yan
For fixed $\beta>1$ and $\alpha\in[0,1)$, each $x\in[0,1]$ has an \emph{intermediate $\beta$-expansion} of the form $x=\sum_{i=1}^\infty\frac{c_i-\alpha}{\beta^i}$. Each such expansion produces for the number $x$ a sequence of approximations $\left(\
Externí odkaz:
http://arxiv.org/abs/2409.14428
We define two types of the $\alpha$-Farey maps $F_{\alpha}$ and $F_{\alpha, \flat}$ for $0 < \alpha < \tfrac{1}{2}$, which were previously defined only for $\tfrac{1}{2} \le \alpha \le 1$ by R.~Natsui (2004). Then, for each $0 < \alpha < \tfrac{1}{2}
Externí odkaz:
http://arxiv.org/abs/2405.10921
We revisit Ito's (\cite{I1989}) natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a slight shift in perspective on the order in which these convergents and med
Externí odkaz:
http://arxiv.org/abs/2312.13988
Publikováno v:
Phys. Rev. B 108, 104204 (2023)
We introduce two 1D tight-binding models based on the Tribonacci substitution, the hopping and on-site Tribonacci chains, which generalize the Fibonacci chain. For both hopping and on-site models, a perturbative real-space renormalization procedure i
Externí odkaz:
http://arxiv.org/abs/2304.11144
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction. We discus
Externí odkaz:
http://arxiv.org/abs/2303.07777
Autor:
Dajani, Karma, Sanderson, Slade
We study a one-parameter family of interval maps $\{T_\alpha\}_{\alpha\in[1,\beta]}$, with $\beta$ the golden mean, defined on $[-1,1]$ by $T_\alpha(x)=\beta^{1+|t|}x-t\beta\alpha$ where $t\in\{-1,0,1\}$. For each $T_\alpha,\ \alpha>1$, we construct
Externí odkaz:
http://arxiv.org/abs/2301.08623
We consider the iterated function system (IFS) $$f_{\vec{q}}(\vec{z})=\frac{\vec{z}+\vec{q}}{\beta},\vec{q}\in\{(0,0),(1,0),(0,1)\}.$$ As is well known, for $\beta = 2$ the attractor, $S_\beta$, is a fractal called the Sierpi\'nski gasket(or sieve) a
Externí odkaz:
http://arxiv.org/abs/2201.07560
Autor:
Dajani, Karma, Langeveld, Niels
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the underlying
Externí odkaz:
http://arxiv.org/abs/2112.04275
Autor:
Dajani, Karma, Power, Kieran
We consider the random $\beta$-transformation $K_{\beta}$, defined on $\{0,1\}^{\mathbb N}\times[0, \frac{\lfloor\beta\rfloor}{\beta-1}]$, that generates all possible expansions of the form $x=\sum_{i=0}^{\infty}\frac{a_i}{\beta^i}$, where $a_i\in \{
Externí odkaz:
http://arxiv.org/abs/2104.11634
We generalize the greedy and lazy $\beta$-transformations for a real base $\beta$ to the setting of alternate bases $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, which were recently introduced by the first and second authors as a particular case
Externí odkaz:
http://arxiv.org/abs/2102.08627