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This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted con- straint satisfaction problems (CSPs), as well as more…
Following McShane, we employ the stable norm on the homology of the modular torus to investigate the Markov ordering on the set of relatively prime integer pairs $(q,p)$ with $q\ge p\ge0$. Our main theorem is a characterization of slopes…
We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally…
We study infinite systems of mean field weakly coupled intermittent maps in the Pomeau-Manneville scenario. We prove that the coupled system admits a unique ``physical'' stationary state, to which all absolutely continuous states converge.…
This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…
Maps $f,g\colon I\to I$ are called strongly commuting if $f\circ g^{-1}=g^{-1}\circ f$. We show that strongly commuting, piecewise monotone maps $f,g$ can be decomposed into a finite number of invariant intervals (or period 2 intervals) on…
The cost functions considered are $c(x,y)=h(x-y)$, where $h\in C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and…
It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…
We consider in this article the properties of the topological conjugacy of the piecewise linear unimodal maps $g:\, [0,\, 1]\rightarrow [0,\, 1]$, all whose kinks belong to the complete pre-image of $0$. We call such maps firm carcass maps.…
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…
A class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure.
We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…
This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of…
The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary,…
We consider the topological behaviors of continuous maps with one topological attractor on compact metric space $X$. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals…
Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar…
We investigate the flexibility of the entropy (topological and metric) for the class of piecewise expanding unimodal maps. We show that the only restrictions for the values of the topological and metric entropies in this class are that both…