Misiurewicz point patterns generation in one-dimensional quadratic maps

G. Pastor, M. Romera, G. Alvarez and F. Montoya

Physica A: Statistical Mechanics and its Applications, 2001, vol. 292, issue 1, 207-230

Abstract: In a family of one-dimensional quadratic maps, Misiurewicz points are unstable and the orbits of such a points are repulsive. On the contrary, the orbits of superstable periodic points are attractive. Here we study the patterns of the symbolic sequences of both Misiurewicz and superstable periodic points, and show that a Misiurewicz point pattern can be obtained as the limit of the sum of a superstable periodic orbit pattern plus itself or some of its heredity transmitters repeated an infinite number of times. Inversely, when a Misiurewicz point pattern is given, we also show that it is possible to find both the superstable periodic orbit pattern and the heredity transmitters that generate such a pattern.

Keywords: One-dimensional quadratic maps; Periodic orbits generation; Mandelbrot set antenna; Misiurewicz points (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100005860
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:292:y:2001:i:1:p:207-230

DOI: 10.1016/S0378-4371(00)00586-0

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().