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Geometric correlations and multifractals

Technical Report:

Abstract

There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs.
Authors:
Publication Date:
Jul 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/154
Reference Number:
SCA: 661000; PA: AIX-22:081531; SN: 91000608728
Resource Relation:
Other Information: PBD: Jul 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; FRACTALS; ATTRACTORS; DYNAMICS; 661000; GENERAL PHYSICS
OSTI ID:
10105544
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92609039; TRN: XA9129674081531
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
35 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Amritkar, R E. Geometric correlations and multifractals. IAEA: N. p., 1991. Web.
Amritkar, R E. Geometric correlations and multifractals. IAEA.
Amritkar, R E. 1991. "Geometric correlations and multifractals." IAEA.
@misc{etde_10105544,
title = {Geometric correlations and multifractals}
author = {Amritkar, R E}
abstractNote = {There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs.}
place = {IAEA}
year = {1991}
month = {Jul}
}