Related papers: Invariant measures for Cherry flows
Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…
Srinivas [Commun. Math. Phys. 71 (1980), 131-158] proposed a postulate in quantum mechanics that extends the von Neumann-Lueders collapse postulate to observables with continuous spectrum. His collapse postulate does not determine a unique…
We present and analyze rigorously a quadratically convergent algorithm to compute an invariant circle for 2-dimensional maps along with the corresponding foliation by stable manifolds. We prove that when the algorithm starts from an initial…
The paper is devoted to the isotropic realizability of a regular gradient field u or a more general vector field b, namely the existence of a continuous positive function $\sigma$ such that $\sigma$b is divergence free in R d or in an open…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. The main results of this article are that a planar (regular) wandering flow has no generalized…
Realizing stable two-dimensional (2D) Dirac points against spin-orbit coupling (SOC) has attracted much attention because it provides a platform to study the unique transport properties. In previous work, Young and Kane [Phys. Rev. Lett.…
Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system. For topological materials described by Dirac…
We prove the upper semicontinuity of the measure theoretic entropy for the geodesic flow on complete Riemannian manifolds without focal points and bounded sectional curvature. We then study the relationship between the escape of mass…
We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial guesses. No preferred coordinate system is required, meaning…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
We consider a random walk on a closed manifold $M$ driven by a probability measure $\mu$ on the space of $C^2$ diffeomorphisms. Provided $\mu$ has compact support, satisfies certain gap and pinching conditions, and is weak-$*$ close to a…
The purpose of this paper is two-fold. First, to provide a straightforward proof of the Cauchy's invariants (CIs) from the particle relabeling symmetry of the action functional for rotational barotropic flows, using pure geometric…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
Any Borel probability measure supported on a Cantor set of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs…
This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in…
We study the topology of the space of probability measures invariant under the geodesic flow, defined on the unit-tangent bundle of a compact Riemannian manifold with non-positive curvature. Building on a previous work by Coud\`ene and…
We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of…
Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant…
We prove that for a polynomial diffeomorphism of C^2 , the support of any invariant measure, apart from a few obvious cases, is contained in the closure of the set of saddle periodic points.