Gibbs Measures and Power Spectra for Type I Intermittent Maps
نویسندگان
چکیده
Gibbs measures of dynamical systems are investigated using the corresponding correlation function and power spectrum. The method is shown to be equivalent to the concept of order{q power spectra which has been developed previously. A technique for the computation of these spectra is presented. As an application we specially focus on the treatment of type I intermittent model maps and investigate their phase transition. In the vicinity of the phase transition point the order{q power spectra are shown to obey some typical scaling relation which is captured neither by the topological pressure nor by the ordinary power spectrum.
منابع مشابه
A Multifractal Analysis of Gibbs Measures for Conformal Expanding Maps and Markov Moran Geometric Constructions
We establish the complete multifractal formalism for Gibbs measures for confor-mal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic Julia sets, and conformal toral endomorphisms. This paper describes the multifractal analysis of measures invariant under dynamical systems. The concept of a multifractal analysis was suggested by seve...
متن کاملLarge Deviations Bounds for Non-uniformly Hyperbolic Maps and Weak Gibbs Measures
We establish bounds for the measure of deviation sets associated to continuous observables with respect to weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms.
متن کاملErdös-Rényi laws for dynamical systems
We establish Erdös-Rényi limit laws for Lipschitz observations on a class of non-uniformly expanding dynamical systems, including logistic-like maps. These limit laws give the maximal average of a time series over a time window of logarithmic length. We also give results on maximal averages of a time series arising from Hölder observations on intermittent-type maps over a time window of polynom...
متن کاملCOSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES
Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2...
متن کاملEffects of Destriping Errors on CMB Polarisation Power Spectra and and Pixel Noise Covariances
Low frequency detector noise in CMB experiments must be corrected to produce faithful maps of the temperature and polarization anisotropies. For a Planck-type experiment the low frequency noise corrections lead to residual stripes in the maps. Here I show that for a ring torus and idealised detector geometry it is possible to calculate analytically the effects of destriping errors on the temper...
متن کامل