相关论文: Non-Injectivity of Infinite Interval Exchange Tran…

We show that the typical measure preserving transformation is not isomorphic to any interval exchange transformation.

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…

Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…

Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.

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…

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions…

We study nonperiodic tilings of the line obtained by a projection method with an interval projection structure. We obtain a geometric characterisation of all interval projection tilings that admit substitution rules and describe the set of…

We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE matrix has a null infinitesimal distribution. Moreover, we…

This paper establishes topological (equi-)semiconjugacy and (equi-)conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. First, some necessary and sufficient conditions are given for a non-autonomous…

This is a mini-review about generalized instantons of noncommutative gauge theories in dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their geometric interpretations, and their applications to the…

We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as…

We consider generalized interval exchange transformations, or briefly GIETs, that is bijections of the interval which are piecewise increasing homeomorphisms with finite branches. When all continuous branches are translations, such maps are…

We study the group IET of all interval exchange transformations. Our first main result is that the group generated by a generic pairs of elements of IET is not free (assuming a suitable irreducibility condition on the underlying…

For an interval exchange map, the number of discontinuities of its iterates either exhibits linear growth or is bounded. This dichotomy is used to prove that the group of interval exchanges does not contain distortion elements, giving…

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear…

We introduce a new concept of interval rearrangement ensembles (IRE), which is a generalization of interval exchange transformations (IET). This construction expands the space of IETs in accordance with the natural duality that we pinpoint.…

We characterize discrete (anti-)unitary symmetries and their non-invertible generalizations in $2+1$d topological quantum field theories (TQFTs) through their actions on line operators and fusion spaces. We explain all possible sources of…

In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we…

Generalized interval exchange transformations (GIETs) are semi-conjugate to interval exchange transformations (IETs) when the Rauzy-Veech combinatorics is $\infty$-complete. When this semi-conjugacy is a homeomorphism, a fundamental problem…

We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular…