Related papers: Discontinuity growth of interval exchange maps
A disjoint rotation map is an interval exchange transformation (IET) on the unit interval that acts by rotation on a finite number of invariant subintervals. It is currently unknown whether the group E of all IETs possesses any non-abelian…
Given an orientation-preserving diffeomorphism of the interval [0;1], consider the uniform norm of the differential of its n-th iteration. We get a function of n called the growth sequence. Its asymptotic behaviour is an interesting…
Given a diffeomorphism of the interval, consider the uniform norm of the derivative of its n-th iteration. We get a sequence of real numbers called the growth sequence. Its asymptotic behavior is an invariant which naturally appears both in…
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval…
A perturbed family of interval exchange maps (FIEMs) provides a natural two-\linebreak{}dimensional area-preserving extension of interval exchange maps, with each IEM parameterized by an action variable $y$. Such families arise, for…
We study discontinuous interval maps generated by the action of erasing block substitutions on the binary expansion. After establishing some general properties of these maps, we categorize erasing block substitutions in a hierarchy of…
We obtain several results on the distortion asymptotics for the iterations of diffeomorphisms of the interval extending the recent work of Polterovich and Sodin.
We relate the Mather invariant of diffeomorphisms of the (closed) interval to their asymptotic distortion. For maps with only parabolic fixed points, we show that the former is trivial if and only if the latter vanishes. As a consequence,…
We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts,…
The representation sets of central loops are investigated and the results obtained are used to construct a finite C-loop. It is shown that for certain types of isotopisms, the central identities are isotopic invariant.
We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.
Interval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the star-discrepancy. Few examples of interval exchange…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
We investigate the question of which growth rates are possible for the number of periodic points of a compact group automorphism. Our arguments involve a modification of Linnik's Theorem, concerning small prime numbers in arithmetic…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…
A distribution of points that satisfies the property of local isotropy is not necessarily homogeneous: homogeneity is implied by the condition of local isotropy together with the assumption of analyticity or regularity. Here we show that…
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
Let E denote the group of all interval exchange transformations on [0,1). Given a suitable topological group structure on E, it is possible to classify all one-parameter interval exchange actions (continuous homomorphisms from R to E). In…