Best simultaneous Diophantine approximations for some pairs of algebraic numbers
We compute the sequence of best Diophantine approximations for some pairs of cubic Pisot numbers which do not satisfy the Property (F).
math.NT↗
arXiv subjects
Gustavo Antonio Pavani
Publications and source records attributed to Gustavo Antonio Pavani.
On a class of Rauzy fractals without the finiteness property
We present some topological and arithmetical aspects of a class of Rauzy fractals $\mathcal{R}_{a,b}$ related to the polynomials of the form $P_{a,b}(x)=x^{3}-ax^{2}-bx-1$, where $a$ and $b$ are integers satisfying $-a+1 \leq b \leq -2$. This class has the property that $0$ lies on the boundary of $\mathcal{R}_{a,b}$. We construct explicit finite automata that recognize the boundaries of these fractals, which allows to establish the number of neighbors of $\mathcal{R}_{a,b}$. In particular, we prove that if $2a+3b+4 \leq 0$ then $\mathcal{R}_{a,b}$ is not homeomorphic to a topological disk. We also show that the boundary of the set $\mathcal{R}_{3,-2}$ is generated by two infinite iterated function systems.
math.DS↗