Intra-orbit separation of dense orbits of interval maps

Manjunath, G. ; Ganesh, Sista Sivaji ; Anand, G. V. (2006) Intra-orbit separation of dense orbits of interval maps Aequationes Mathematicae, 72 (1-2). pp. 89-99. ISSN 0001-9054

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Official URL: http://www.springerlink.com/content/h2k1w1728rl25l...

Related URL: http://dx.doi.org/10.1007/s00010-006-2847-5

Abstract

We introduce the notion of intra-orbit separation for the orbits of continuous transitive maps on a compact interval to demonstrate separation of two points on a given dense orbit. We associate a non-negative real number γ with a transitive interval map ƒ called the separation index of the map ƒ. For a transitive map ƒ having at least two fixed points we show: (i) the separation index γ is positive, (ii) for every 0 < τ < γ and any pair of distinct points xj and xl on a dense orbit, (xj, xl) is a Li-Yorke pair of modulus τ, that is, lim supn→+∞n(x) - ƒn(y)| > τ and lim infn→+∞|ƒn(x) − ƒn(y)| = 0.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Chaos; Li-Yorke Pairs; Sensitivity
ID Code:89733
Deposited On:30 Apr 2012 20:23
Last Modified:30 Apr 2012 20:23

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