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In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma which is a characterization of the Congruence Modular Varieties among all the variety of Universal Algebra, introduced in (Gumm, 1983). Starting from a…

Category Theory · Mathematics 2021-03-24 Dominique Bourn

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

Complex Variables · Mathematics 2021-09-28 Olli Hirviniemi , István Prause , Eero Saksman

We obtain sharp rotation bounds for homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ whose distortion is in $L^p_{loc}$, $p\geq1$, and whose inverse have controlled modulus of continuity. The motivation to study this class of maps comes from…

Dynamical Systems · Mathematics 2025-12-23 Lauri Hitruhin , Banhirup Sengupta

We study the asymptotical behaviour of iterates of piecewise contractive maps of the interval. It is known that Poincar\'e first return maps induced by some Cherry flows on transverse intervals are, up to topological conjugacy, piecewise…

Dynamical Systems · Mathematics 2014-07-09 Arnaldo Nogueira , Benito Pires

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not…

Dynamical Systems · Mathematics 2017-11-20 Gianluigi Del Magno , João Lopes Dias , Pedro Duarte , José Pedro Gaivão

The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs. These and other results usually rely on the fact that every robustly…

Combinatorics · Mathematics 2018-08-23 Allan Lo , Viresh Patel

This paper is concerned with the wave length $\lambda$ of smooth periodic traveling wave solutions of the Camassa-Holm equation. The set of these solutions can be parametrized using the wave height $a$ (or "peak-to-peak amplitude"). Our…

Dynamical Systems · Mathematics 2015-03-10 Anna Geyer , Jordi Villadelprat

In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…

General Topology · Mathematics 2024-06-13 Mikhail Yourievich Liseev

We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…

Symplectic Geometry · Mathematics 2023-10-23 Abror Pirnapasov , Rohil Prasad

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

Dynamical Systems · Mathematics 2012-04-10 Nguyen Tien Zung , Nguyen Van Minh

Our start point is a 3D piecewise smooth vector field defined in two zones and presenting a shared fold curve for the two smooth vector fields considered. Moreover, these smooth vector fields are symmetric relative to the fold curve, giving…

Dynamical Systems · Mathematics 2017-02-07 Tiago Carvalho , Bruno Rodrigues de Freitas

For every $r\in\mathbb{N}_{\geq 2}\cup\{\infty\}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with 1-dimensional orientation preserving center bundle. To be…

Dynamical Systems · Mathematics 2023-09-06 Yi Shi , Xiaodong Wang

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

Differential Geometry · Mathematics 2019-04-02 Andreas Bernig

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…

Differential Geometry · Mathematics 2015-10-22 David Glickenstein

For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric…

Geometric Topology · Mathematics 2018-09-05 Sergey Fomin , Dylan Thurston

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

Dynamical Systems · Mathematics 2024-02-27 Maxim Arnold , Lael Costa , Serge Tabachnikov

For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of…

Dynamical Systems · Mathematics 2019-01-08 Lluís Alsedà , Sylvie Ruette

We study the non-wandering set of $C^3$ contracting Lorenz maps $f$ with negative Schwarzian derivative. We show that if $f$ doesn't have attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a…

Dynamical Systems · Mathematics 2014-02-13 Paulo Brandão

The isomonodromic deformations underlying the Painlev\'e transcendants are interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop algebra $\tilde\grg$ in the classical $R$-matrix framework. It is shown how canonical…

High Energy Physics - Theory · Physics 2008-02-03 J. Harnad , M. -A. Wisse

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…

Differential Geometry · Mathematics 2008-09-17 M. Benyounes , E. Loubeau , L. Todjihounde
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