Related papers: Two remarks on the Shrinking Target Property

We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…

Let $(M^n_i, g_i)\to (X,d_X)$ be a Gromov-Hausdorff converging sequence of Riemannian manifolds with ${\rm Sec}_{g_i} \ge -1$, ${\rm diam}\, (M_i)\le D$, and such that the $M^n_i$ are all homeomorphic to tori $T^n$. Then $X$ is homeomorphic…

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…

In this paper we investigate the strict convexity and the differentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly…

We prove that the return map of the unstable horocycle flow on the space of horizontally short translation surfaces associated to a lattice surface $(X, \omega)$ is weakly mixing. This extends a result of Cheung-Quas for the square torus to…

The field of C*-algebras over the interval [0,2] for which the fibers are the Soft Tori is shown to be continuous. This result is applied to show that any pair of non-commuting unitary operators can be perturbed (in a weak sense) in such a…

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of C^m into P^n with (3n+1) moving targets and truncated multiplicities.

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…

We use variational methods and a modified curvature flow to give an alternative proof of the existence of a self-shrinking torus under mean curvature flow. As a consequence of the proof, we establish an upper bound for the weighted energy…

Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…

We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…

We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the…

It is well known that attributed tree transducers can be equipped with "regular look-around" in order to obtain a more robust class of translations. We present two characterizations of this class in terms of macro tree transducers (MTTs):…

We wish to tile a rectangle or a torus with only vertical and horizontal bars of a given length, such that the number of bars in every column and row equals given numbers. We present results for particular instances and for a more general…

We study the existence of whiskered tori in a family $f_\mu$ of conformally symplectic maps depending on parameters $\mu$. Whiskered tori are tori on which the motion is a rotation, but they have as many expanding/contracting directions as…

In this paper, we show that the ground-state density of any non-interacting Schr\"odinger operator on the one-dimensional torus with potentials in a certain class of distributions is strictly positive. This result together with recent…

We describe the shrinking target problem for random iterated function systems which semi-conjugate to a random subshifts of finite type. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The…

In this paper, using Klyachko's classification theorem we study positivity and semi-stability of toric vector bundles on a class of nonsingular projective toric varieties, known as Bott towers. In particular, we give a criterion of $s$-jet…

Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive…