Sums of variables at the onset of chaos

Date

2014

Type:

Artículo

item.page.extent

item.page.accessRights

item.contributor.advisor

ORCID:

Journal Title

Journal ISSN

Volume Title

Publisher

item.page.isbn

item.page.issn

item.page.issne

item.page.doiurl

item.page.other

item.page.references

Abstract

We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the perioddoubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.

Description

item.page.coverage.spatial

item.page.sponsorship

Citation

The European Physical Journal B, 2014, vol. 87, n° 32, 7 p.

Keywords

Statistical, Nonlinear Physics

item.page.dc.rights

item.page.dc.rights.url