D\'ecroissance exponentielle des corr\'elations pour un syst\`eme dynamique r\'eel induit d'un syst\`eme en dimension 2

TL;DR

This paper investigates how correlations decay exponentially in a real-valued discrete dynamical system defined by a second order recurrence, under specific analytical conditions on the recurrence function.

Contribution

It establishes exponential decay of correlations for a class of second order recurrence relations with analytical properties, extending understanding of dynamical behavior in such systems.

Findings

Correlations decay exponentially under certain conditions

Decay rate depends on regularity and bounds of the recurrence function

Provides analytical criteria for correlation decay in second order systems

Abstract

We study the discrete-time, real valued bounded process $\{X_n, n\in {\mathbb N} \}$ defined by a second order recurrence relation $X_{n+2} = \varphi(X_n,X_{n+1})$. We obtain the decay of correlations under analytical hypotheses on $\varphi $ (regularity, bounds on derivatives ...)