Related papers: Piecewise rotations: limit set for the non -biject…

We give quantitative bounds for the number of quasi-integral points in orbits of semigroups of rational maps under some conditions, generalizing previous work of L. C. Hsia and J. Silverman (2011) for orbits generated by the iterations of…

In this paper we study certain groups of bilipschitz maps of the boundary minus a point of a negatively curved space that is an abelian-by-cyclic solvable Lie group, where the extension is given by a matrix whose eigenvalues all lie outside…

In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the…

The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…

We study the scaling limits of looptrees associated with Bienaym\'e--Galton--Watson (BGW) trees, that are obtained by replacing every vertex of the tree by a "cycle" whose size is its degree. First, we consider BGW trees whose offspring…

We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-slide" operation. This is the first time a bijective proof is…

I introduced the notions of proper and piecewise proper families of reals to make progress on an open question in the field of models of PA about whether every Scott set is the standard system of a model of PA. A family of reals X is proper…

Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…

Let G be an algebraic group corresponding to a compact Lie group. We study the restiction map from the Chow ring CH(BG) to the Wely group invariants CH(BT)^W. For example, we note that if G is simply connect and H(G) has torsion, then the…

In this short note we construct unbounded families of minimal surfaces of general type with canonical map of degree 4 such that the limits of the slopes assume countably many different values among 6+2/3 and 8.

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we…

The allowed patterns of a map are those permutations in the same relative order as the initial segments of orbits realized by the map. In this paper, we characterize and provide enumerative bounds for the allowed patterns of signed shifts,…

We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…

We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…

We study the set ${\cal D}(\Phi)$ of limit directions of a vector cocycle $(\Phi_n)$ over a dynamical system, i.e., the set of limit values of $\Phi_n(x) /\|\Phi_n(x)\|$ along subsequences such that $\|\Phi_n(x)\|$ tends to $\infty$. This…

We compute two invariants of topological conjugacy, the upper and lower limits of the inverse of Boshernitzan's ne_n, where e_n is the smallest measure of a cylinder of length n, for three families of symbolic systems, the natural codings…

We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary…

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…

We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…

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…