Which orbit types force only finitely many orbit types?

Kannan, V.; Mandal, Pabitra Narayan

doi:10.1080/10236198.2020.1784152

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…It throws further light on the forcing relation on the orbit-patterns. It is no longer a partial order (though it was partial order in some other instances [6], [2]).…”

Section: Characterization Of Universal Functionsmentioning

confidence: 99%

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Universal functions for the Sharkovsky classes of maps

Kannan¹,

Mandal²

2021

Preprint

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We exhibit a single interval map (called universal map) that admits all those orbit patterns which are available in the first Sharkovsky class. An interval map is said to be in the first Sharkovsky class if every periodic point of it is a fixed point. This provides a way to find universal maps in the class of contractions on interval. We also characterize all such universal maps in the first Sharkovsky class. However, this result is not true in higher Sharkovsky classes, i.e., there is no universal function for n-th Sharkovsky class when n > 1.

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“…It throws further light on the forcing relation on the orbit-patterns. It is no longer a partial order (though it was partial order in some other instances [6], [2]).…”

Section: Characterization Of Universal Functionsmentioning

confidence: 99%

“…Some families F admit universal elements and some others do not. For instance, if F is the class of t-simple systems on R, there is no universal element in it (see [6]). As a note, in topological dynamics a similar idea of universality with respect to ω-limit sets appeared earlier.…”

Section: Introductionmentioning

confidence: 99%

Universal functions for the Sharkovsky classes of maps

Kannan¹,

Mandal²

2021

Preprint

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“…This paper is also a sequel to [10], [5], and [1] where the orbit-patterns of some simple dynamical systems have been investigated. In those papers, the classes of interval maps studied were i) those with the zero entropy ii) those with only finitely many types of orbits iii) those with only three or four non-ordinary points (and therefore with only 3 or 4 types of orbits).…”

mentioning

confidence: 99%

Interval maps where every point is eventually fixed

Kannan¹,

Mandal²

2020

Preprint

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Among the orbit patterns that force only eventually fixed trajectories, we completely describe the forcing relation, by answering the question: which orbit patterns force which others? (for details see [7])). In another [2] it is the language of locating periodic points of period 1 and 2. In yet another [6], it is an index set for the set of orbit-patterns. Statement of Main Result.There is a natural bijection between the language {L, R} * and the set of all EF orbit patterns. The forcing relation on the latter set receives a neat description when framed in the terminology of theory of languages. We are able to find four rules of derivation in {L, R} * so that the following theorem becomes true: An orbit pattern α forces another orbit pattern β if and only if the corresponding word of β can be derived from that of α using four rules of derivation (described below).

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Interval maps where every point is eventually fixed

Kannan

Mandal

2022

Proc Math Sci

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Which orbit types force only finitely many orbit types?

Cited by 6 publications

References 5 publications

Universal functions for the Sharkovsky classes of maps

Universal functions for the Sharkovsky classes of maps

Interval maps where every point is eventually fixed

Interval maps where every point is eventually fixed

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