Omega-limit sets for shift spaces and unimodal maps

On α-Limit Sets in Lorenz Maps

Entropy ◽

10.3390/e23091153 ◽

2021 ◽

Vol 23 (9) ◽

pp. 1153

Author(s):

Łukasz Cholewa ◽

Piotr Oprocha

Keyword(s):

Topological Entropy ◽

Dynamical Behavior ◽

Unimodal Maps ◽

Limit Sets ◽

Lorenz Maps ◽

Provided Examples

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.

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Limit sets ofS-unimodal maps with zero entropy

Communications in Mathematical Physics ◽

10.1007/bf01205554 ◽

1987 ◽

Vol 110 (4) ◽

pp. 655-659 ◽

Cited By ~ 14

Author(s):

John Guckenheimer

Keyword(s):

Unimodal Maps ◽

Limit Sets ◽

Zero Entropy

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Countable inverse limits of postcritical $w$-limit sets of unimodal maps

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2010.27.1059 ◽

2010 ◽

Vol 27 (3) ◽

pp. 1059-1078 ◽

Cited By ~ 1

Author(s):

Chris Good ◽

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Robin Knight ◽

Brian Raines ◽

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...

Keyword(s):

Inverse Limits ◽

Unimodal Maps ◽

Limit Sets

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Countable limit sets of unimodal maps

Journal of Dynamical and Control Systems ◽

10.1007/s10883-010-9095-7 ◽

2010 ◽

Vol 16 (3) ◽

pp. 319-328

Author(s):

T. Inaba ◽

Y. Kano

Keyword(s):

Unimodal Maps ◽

Limit Sets

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Length distortion and the Hausdorff dimension of limit sets

American Journal of Mathematics ◽

10.1353/ajm.2000.0016 ◽

2000 ◽

Vol 122 (3) ◽

pp. 465-482 ◽

Cited By ~ 1

Author(s):

Martin Bridgeman ◽

Edward C. Taylor

Keyword(s):

Hausdorff Dimension ◽

Limit Sets ◽

Length Distortion

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A non-Borel special alpha-limit set in the square

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2021.68 ◽

2021 ◽

pp. 1-11

Author(s):

STEPHEN JACKSON ◽

BILL MANCE ◽

SAMUEL ROTH

Keyword(s):

Dynamical Systems ◽

Limit Set ◽

Limit Sets ◽

Unit Square

Abstract We consider the complexity of special $\alpha $ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.

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Limit Behavior of Solutions of Ordinary Linear Differential Equations

Georgian Mathematical Journal ◽

10.1515/gmj.1994.315 ◽

1994 ◽

Vol 1 (3) ◽

pp. 315-323

Author(s):

František Neuman

Keyword(s):

Differential Equations ◽

Oscillatory Behavior ◽

Linear Differential Equations ◽

Limit Behavior ◽

Limit Sets ◽

Equivalent Linear ◽

Linear Differential ◽

Ordinary Linear Differential Equations

Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.

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A Full Description of ω-Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications

Mathematics ◽

10.3390/math9040452 ◽

2021 ◽

Vol 9 (4) ◽

pp. 452

Author(s):

Antonio Linero-Bas ◽

María Muñoz-Guillermo

Keyword(s):

Economic Models ◽

Full Description ◽

Cournot Model ◽

Empty Interior ◽

Limit Sets ◽

Economic Applications

Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, we give a full description of its ω-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω-limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω-limits that appear.

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