相关论文: Coding rotations on intervals
We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
Lambda words are sequences obtained by encoding the differences between ordered elements of the form i+j\theta, where i and j are non-negative integers and 1 < \theta <2. Lambda words are right-infinite words defined over an infinite…
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
We characterize cutting sequences of infinite geodesics on square-tiled surfaces by considering interval exchanges on specially chosen intervals on the surface. These interval exchanges can be thought of as skew products over a rotation,…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…
An infinite permutation $\alpha$ is a linear ordering of $\mathbb N$. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this…
We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of {\pi}/n. We find new substitution rules admitting 7-fold rotational symmetry at many different…
Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words,…
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintuple $\p$ of real numbers satisfying inequations. Viewing…
We show that any automatic sequence can be separated into a structured part and a Gowers uniform part in a way that is considerably more efficient than guaranteed by the Arithmetic Regularity Lemma. For sequences produced by strongly…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to…
For any positive integer $n$ along with parameters $\alpha$ and $\nu$, we define and investigate $\alpha$-shifted, $\nu$-offset, floor sequences of length $n$. We find exact and asymptotic formulas for the number of integers in such a…
We review a series of forthcoming results leading to the construction of a natural evolution on the space of loops with values in a Riemannian manifold. In particular, this clarifies the algebraic structure of the renormalisation procedures…
Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-integrable limit, or alternatively from the horseshoe. Given…
An $(m, n)$-parking function can be characterized as function $f:[n] \to [m]$ such that the partition obtained by reordering the values of $f$ fits inside a right triangle with legs of length $m$ and $n$. Recent work by McCammond, Thomas,…
Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…