Related papers: On the relationship between Lozi maps and max-type…
Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We prove a Lefschetz-type coincidence theorem: if the Lefschetz…
In this expository paper, we provide an intuition and illustration-driven overview of two recent results that tie the dynamics of certain homeomorphisms of infinite-type surfaces, called end-periodic homeomorphisms, to the geometry of their…
In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and…
We prove that for any nondegenerate dendrite $D$ there exist topologically mixing maps $F : D \to D$ and $f : [0, 1] \to [0, 1]$, such that the natural extensions (aka shift homeomorphisms) $\sigma_F$ and $\sigma_f$ are conjugate, and…
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
In this work, we obtained separation results via codimension-1 maps to generalized manifolds. More specifically, we proved results that allow us to estimate the number of connected components of the complement of the image of such maps.
It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.
The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
The analytical structure of some generalizations of the circle map is given. Also a generalization of off centre reflection is studied. The stability of Ito-Glass coupled map lattice is studied.
We investigate the dynamical properties of cusp bifurcations in max-plus dynamical systems derived from continuous differential equations through the tropical discretization and the ultradiscrete limit. A general relationship between cusp…
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…
In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps…
We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…
We introduce a factorization for the map between moduli spaces of stable maps which forgets one marked point. This leads to a study of universal relations in the cohomology of stable map spaces in genus zero.
We extend Osserman's lemma on the generalized Gauss map of two-dimensional minimal graphs of higher codimension, construct a Jenkins-Serrin type special Lagrangian Scherk graph explicitly, and generalize Calabi's correspondence between…
A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that $\eta_i:\X_i\to \X_i$ is a continuous proper map on a locally compact…
We investigate generalized phase transitions of type localization - delocalization from one to several Sinai-Bowen-Ruelle invariant measures in finite networks of chaotic elements (coupled map lattices) with general graphs of connections in…