Related papers: Mean field coupled dynamical systems: Bifurcations…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…
We study infinite systems of globally coupled Anosov diffeomorphisms with weak coupling strength. Using transfer operators acting on anisotropic Banach spaces, we prove that the coupled system admits a unique physical invariant state,…
We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a N-pole-to-S-pole map of the circle. Leveraging…
Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant…
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with…
Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in…
We treat Mechanics as a 1-dimensional general-relativistic gauge field theory, Mechanical Field Theory (MFT), introducing what we call the Mechanical Field Space (MFS) and exploiting its bundle geometry. The diffeomorphism covariance of MFT…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…
Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in…