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Abstract: We introduce the fundamental group ${\mathcal F}(\mathcal{R}_{G, \phi})$ of a uniquely ergodic Cantor minimal $G$-system $\mathcal{R}_{G, \phi}$ where $G$ is a countable discrete group. We c...
Epidemic Spread in Human Networks     Epidemic Spread  Human Networks  Dynamical Systems       font style='font-size:12px;'> 2011/10/8
Abstract: One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to desc...
Abstract: In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stres...
Abstract: We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The...
Abstract: The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by P. Hubert...
Abstract: In this paper we present a unifying geometric framework for modeling various sorts of physical network dynamics as port-Hamiltonian systems. Basic idea is to associate with the incidence mat...
Abstract: Matchbox manifolds ${\mathfrak M}$ are a special class of foliated spaces, which includes as special examples the weak solenoids, and tiling spaces associated to aperiodic tilings with finit...
Diffusion for the periodic wind-tree model     Billiards  diffusion  translations surfaces  Lyapunov exponents  ergodic averages       font style='font-size:12px;'> 2011/8/31
Abstract: The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of the scatter...
Periodically fighting shake, rattle and roll     Dynamical Systems  Periodically  rattle and roll       font style='font-size:12px;'> 2011/8/31
Abstract: How easy is it to suppress shake, rattle and roll in a long bridge or a skyscraper? Most practical structures are designed so that long wave resonance vibrations can be avoided. However, the...
Abstract: When ignorance due to the lack of knowledge, modeled as epistemic uncertainty using Dempster-Shafer structures on closed intervals, is present in the model parameters, a new uncertainty prop...
Abstract: A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method i...
Abstract: We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of $0,1$ sequences, for which the frequency of the pattern 11 in positions $...
Abstract: Let $X$ and $Y$ be compact Kahler manifolds, and let $f:X\rightarrow Y$ be a dominant meromorphic map. We define a pullback operator $f^{\sharp}$ (and its local version) for currents of the ...
Abstract: If $G$ is a Polish group and $\Gamma$ is a countable group, denote by $\Hom(\Gamma, G)$ the space of all homomorphisms $\Gamma \to G$. We study properties of the group $\cl{\pi(\Gamma)}$ for...
Abstract: We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our me...

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