Related papers: Intermittency in two dimensions
This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained…
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
We numerically reexamine the scaling behavior of period doublings in four-dimensional volume-preserving maps in order to resolve a discrepancy between numerical results on scaling of the coupling parameter and the approximate…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
We consider the line, surface and volume elements of fluid in stationary isotropic incompressible stochastic flow in $d$-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a…
We study the transitions to spatio-temporal intermittency in networks of randomly coupled Chate-Manneville maps. The relevant paprameters are the network connectivity, coupling strength, and the local parameter of the map. We show that the…
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…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
In this paper we study the rate of convergence of the iterates of \iid random piecewise constant monotone maps to the time-$1$ transport map for the process of coalescing Brownian motions. We prove that the rate of convergence is given by a…
High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic…
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points.…
We consider several families of long jump random walks on groups of polynomial volume growth which are naturally expected to have a stable-like behavior. We then prove optimal pseudo-Poincar\'e inequalities for these walks. These…