Related papers: A Note on Operator Semigroups Associated to Chaoti…
This paper introduces a new operator relevant to input-output analysis of flows in a statistically steady regime far from the steady base flow: the mean resolvent $\mathbf{R}_0$. It is defined as the operator predicting, in the frequency…
In this paper we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable…
We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the…
The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to…
We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform…
We give a formula relating the $L^2$-isoperimetric profile to the spectral distribution of the Laplace operator associated to a finitely generated group $\Gamma$ or a Riemannian manifold with a cocompact, isometric $\Gamma$-action. As a…
Identifying coherent flow structures in chemical reactors is crucial for understanding the mixing dynamics, which is essential for optimizing reactor performance. We demonstrate the use of a transfer operator method to find coherent flow…
The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism…
The Laplace transform is a widely used tool in the study of probability distributions, often allowing for a probability density functions and distribution functions simpler determination and being a moments generating function. In this…
Let $A$ be the generator of a strongly continuous cosine family $(\cos (tA))_{t\in {\bf R}}$ on a complex Banach space $E$. The paper develops an operational calculus for integral transforms and functions of $A$ using the generalized…
Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a…
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…
We show that the multiplication operator associated to a fractional power of a Gamma random variable, with parameter q>0, maps the convex cone of the 1-invariant functions for a self-similar semigroup into the convex cone of the q-invariant…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
We establish exponential decay in H\"older norm of transfer operators applied to smooth observables of uniformly and nonuniformly expanding semiflows with exponential decay of correlations.
We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…
Since the complexity of the practical environment, many distributed networked systems can not be illustrated with the integer-order dynamics and only be described as the fractional-order dynamics. Suppose multi-agent systems will show the…
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…