Glasnik Matematicki, Vol. 52, No. 2 (2017), 295-329.

OMEGA LIMITS, PROLONGATIONAL LIMITS AND ALMOST PERIODIC POINTS OF A CONTINUOUS FLOW VIA EXTERIOR SPACES

José Manuel García Calcines, Luis Javier Hernández Paricio and María Teresa Rivas Rodríguez

Departamento de Matemáticas, Estadística e I.O., Universidad de La Laguna, 38200 La Laguna, Spain
e-mail: jmgarcal@ull.es

Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain
e-mail: luis-javier.hernandez@unirioja.es

Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain
e-mail: maria-teresa.rivas@unirioja.es

Abstract.   In this paper we analyse some applications of the category of exterior spaces to the study of dynamical systems (flows). The limit space and end space of an exterior space are used to construct different types of limit spaces and end spaces of a dynamical system. In this work we analyse the relationships between the notions and constructions given by the exterior structures of a continuous flow and the more usual notions of omega-limits, first prolongational limits and several types of almost periodic points (Poisson-stable points, non-wandering points) of a flow.

2010 Mathematics Subject Classification.   54H20, 37B99.

Key words and phrases.   Dynamical system, exterior space, exterior flow, limit space functor, end space functor, Freudenthal end point, periodic point, agglomerative point, Poisson-stable point, omega limit, region of attraction, attractor, repeller, non wandering point, first prolongational limit of a point, Lagrange-stable point, dispersive flow, basin of an end point..

Full text (PDF) (free access)

DOI: 10.3336/gm.52.2.09

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