368 research outputs found
Palindromic complexity of codings of rotations
International audienceWe study the palindromic complexity of infinite words obtained by coding rotations on partitions of the unit circle by inspecting the return words. The main result is that every coding of rotations on two intervals is full, that is, it realizes the maximal palindromic complexity. As a byproduct, a slight improvement about return words in codings of rotations is obtained: every factor of a coding of rotations on two intervals has at most 4 complete return words, where the bound is realized only for a finite number of factors. We also provide a combinatorial proof for the special case of complementary-symmetric Rote sequences by considering both palindromes and antipalindromes occurring in it
Bifix codes and interval exchanges
We investigate the relation between bifix codes and interval exchange
transformations. We prove that the class of natural codings of regular interval
echange transformations is closed under maximal bifix decoding.Comment: arXiv admin note: substantial text overlap with arXiv:1305.0127,
arXiv:1308.539
Entropy and Complexity of Polygonal Billiards with Spy Mirrors
We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity
More on the dynamics of the symbolic square root map
In our earlier paper [A square root map on Sturmian words, Electron. J.
Combin. 24.1 (2017)], we introduced a symbolic square root map. Every optimal
squareful infinite word contains exactly six minimal squares and can be
written as a product of these squares: . The square
root of is the infinite word obtained by
deleting half of each square. We proved that the square root map preserves the
languages of Sturmian words (which are optimal squareful words). The dynamics
of the square root map on a Sturmian subshift are well understood. In our
earlier work, we introduced another type of subshift of optimal squareful words
which together with the square root map form a dynamical system. In this paper,
we study these dynamical systems in more detail and compare their properties to
the Sturmian case. The main results are characterizations of periodic points
and the limit set. The results show that while there is some similarity it is
possible for the square root map to exhibit quite different behavior compared
to the Sturmian case.Comment: 22 pages, Extended version of a paper presented at WORDS 201
- …