Related papers: Bounded type interval exchange maps
We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…
The construction of affine interval exchange maps with wandering intervals that are semi-conjugate with a given self-similar interval exchange map is strongly related with the existence of the so called minimal sequences associated with…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
We prove that for infinite rank-one transformations satisfying a property called "partial boundedness," the only commuting transformations are powers of the original transformation. This shows that a large class of infinite…
This paper is concerned with two examples on the application of the free boundary formulation to BVPs on a semi-infinite interval. In both cases we are able to provide the exact solution of both the BVP and its free boundary formulation.…
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
The allowed patterns of a map on a one-dimensional interval are those permutations that are realized by the relative order of the elements in its orbits. The set of allowed patterns is completely determined by the minimal patterns that are…
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having…
We determine a class of rearrangements that admit a supporting tree. This condition implies that the associated rearrangement operator has a bounded vector valued extension. We show that there exists a large subspace of $L^p$ on which a…
Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In…
In this paper we consider the iteration of infinitely many signed exponentials with the same base but the signs may vary. We show that for every base in an explicit interval this iteration converges for any sequence of signs and all the…
The paper is an attempt to generalize a methodology, which is similar to the bounded-input bounded-output method currently widely used for the system stability studies. The presented earlier methodology allows decomposition of input space…
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
By adapting the near-degenerate regime designed by Kahn, Lyubich, and D. Dudko, we prove that the boundaries of Herman rings with bounded type rotation number and of the simplest configuration are quasicircles with dilatation depending only…