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On the topology of the chain recurrent set of a dynamical system

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On the topology of the chain recurrent set of a dynamical system

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Ahmadi, SA. (2014). On the topology of the chain recurrent set of a dynamical system. Applied General Topology. 15(2):167-174. https://doi.org/10.4995/agt.2014.3050

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Metadatos del ítem

Título: On the topology of the chain recurrent set of a dynamical system
Autor: Ahmadi, Seyyed Alireza
Fecha difusión:
Resumen:
[EN] In this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this ...[+]
Palabras clave: Chain recurrent , Chain transitive , Chain component , Inverse limit space.
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2014.3050
Editorial:
Editorial Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2014.3050
Tipo: Artículo

References

N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Recent Advances. North-Holland Math. Library 52. (North-Holland, Amsterdam 1994)

Athanassopoulos, K. (1996). One-dimensional chain recurrent sets of flows in the 2-sphere. Mathematische Zeitschrift, 223(4), 643-649. doi:10.1007/pl00004279

F. Balibrea, J. S. Cánovas and A. Linero, New results on topological dynamics of antitriangular maps, App. Gen. Topol. 2 (2001), 51-61. [+]
N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Recent Advances. North-Holland Math. Library 52. (North-Holland, Amsterdam 1994)

Athanassopoulos, K. (1996). One-dimensional chain recurrent sets of flows in the 2-sphere. Mathematische Zeitschrift, 223(4), 643-649. doi:10.1007/pl00004279

F. Balibrea, J. S. Cánovas and A. Linero, New results on topological dynamics of antitriangular maps, App. Gen. Topol. 2 (2001), 51-61.

Fujita, C., & Kato, H. (2009). Almost periodic points and minimal sets in topological spaces. Applied General Topology, 10(2), 239-244. doi:10.4995/agt.2009.1737

Richeson, D., & Wiseman, J. (2008). Chain recurrence rates and topological entropy. Topology and its Applications, 156(2), 251-261. doi:10.1016/j.topol.2008.07.005

K. Sakai, $C^1$-stably shadowable chain components, Ergodic Theory Dyn. Syst. 28 (2008), 987-1029.

T. Shimomura, On a structure of discrete dynamical systems from the view point of chain components and some applications, Japan. J. Math. (NS) 15 (1989), 99-126.

Wen, X., Gan, S., & Wen, L. (2009). <mml:math altimg=«si1.gif» overflow=«scroll» xmlns:xocs=«http://www.elsevier.com/xml/xocs/dtd» xmlns:xs=«http://www.w3.org/2001/XMLSchema» xmlns:xsi=«http://www.w3.org/2001/XMLSchema-instance» xmlns=«http://www.elsevier.com/xml/ja/dtd» xmlns:ja=«http://www.elsevier.com/xml/ja/dtd» xmlns:mml=«http://www.w3.org/1998/Math/MathML» xmlns:tb=«http://www.elsevier.com/xml/common/table/dtd» xmlns:sb=«http://www.elsevier.com/xml/common/struct-bib/dtd» xmlns:ce=«http://www.elsevier.com/xml/common/dtd» xmlns:xlink=«http://www.w3.org/1999/xlink» xmlns:cals=«http://www.elsevier.com/xml/common/cals/dtd»><mml:msup><mml:mi>C</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>-stably shadowable chain components are hyperbolic. Journal of Differential Equations, 246(1), 340-357. doi:10.1016/j.jde.2008.03.032

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