Related papers: Bounded type interval exchange maps
We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for…
Roth type irrational rotation numbers have several equivalent arithmetical characterizations as well as several equivalent characterizations in terms of the dynamics of the corresponding circle rotations. In this paper we investigate how to…
In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a…
In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can…
We characterize all bounded orbits of two similar Collatz-type quadratic mappings of the set of non-negative integers. In one case, where cycles of all possible lengths may occur, an orbit is bounded if and only if it reaches a cycle. For…
We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it…
A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine…
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…
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 investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
For almost all interval exchange maps T_0, with combinatorics of genus g>=2, we construct affine interval exchange maps T which are semi-conjugate to T_0 and have a wandering interval.
We prove that any over-twist pattern is conjugate to an interval exchange transformation with bounded number of segments of isometry, restricted on one of its cycles. The bound is independent of the period and over-rotation number of the…
Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…
In this paper we investigate translated cone exchange transformations, a new family of piecewise isometries and renormalize its first return map to a subset of its partition. As a consequence we show that the existence of an embedding of an…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
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…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
If the non-zero finite floating-point numbers are interpreted as point intervals, then the effect of rounding can be interpreted as computing one of the bounds of the result according to interval arithmetic. We give an interval…