Let $ M $ be a positive integer and $ q\in (1, M+ 1]. $ We consider expansions of real
numbers in base $ q $ over the alphabet $\{0,\ldots, M\} $. In particular, we study the set …

Let and that this bound is sharp. As a corollary, we give a full description of first-and second-
order critical holes introduced by N. Sidorov [Supercritical holes for the doubling map …

The family of symmetric one sided subshifts in two symbols given by a sequence $ a $ is
studied. We analyse some of their topological properties such as transitivity, the specification …

For a map S: X → XS: X→ X and an open connected set (= a hole) H ⊂ XH⊂ X we define J
_H (S) JH (S) to be the set of points in X whose S-orbit avoids H. We say that a hole H 0 is …

We show that every intermediate β-transformation is topologically conjugate to a greedy β-
transformation with a hole at zero, and provide a counterexample illustrating that the …

We study an intermittent map which has exactly two ergodic invariant densities. The
densities are supported on two subintervals with a common boundary point. Due to certain …

We consider product of expansive Markov maps on an interval with hole which is conjugate
to a subshift of finite type. For certain class of maps, it is known that the escape rate into a …

Abstract Let $ K\subset\mathbb {R} $ be a self-similar set generated by some iterated
function system. In this paper we prove, under some assumptions, that K can be identified …

Let $ K\subseteq\mathbb {R} $ be the unique attractor of an iterated function system. We
consider the case where $ K $ is an interval and study those elements of $ K $ with a unique …

We study the structure of the escape orbits for a certain class of interval maps. This structure
is encoded in the escape transition matrix A< sub> ƒ of an interval map ƒ, extending the …