Related papers: Derivatives and Constraints in Chaotic Flows: Asym…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and, in particular, are conjectured to be equivalent to…
The dynamics of fibres, modelled as a sequence of inertial beads linked via elastic springs, in turbulent flows is dictated by a non-trivial interplay of their inertia and elasticity. Such elastic, inertial fibres preferentially sample a…
Anomalies are known to appear in the perturbation theory for the one-dimensional Anderson model. A systematic approach to anomalies at critical points of products of random matrices is developed, classifying and analysing their possible…
We consider families of diffeomorphisms with dominated splittings and preserving a Borel probability measure, and we study the regularity of the Lyapunov exponents associated to the invariant bundles with respect to the parameter. We obtain…
The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov…
The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
We compare and contrast two types of deformations inspired by mixing applications -- one from the mixing of fluids (stretching and folding), the other from the mixing of granular matter (cutting and shuffling). The connection between…
In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order…
The asymptotic distance between trajectories $d_{\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…
In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…
We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this…
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we provide a…
Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…