Original scientific paper

https://doi.org/10.3336/gm.51.2.12

Dynamic properties for the induced maps on n-fold symmetric product suspensions

Franco Barragán ; Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
Alicia Santiago-Santos ; Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
Jesús F. Tenorio ; Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México

Abstract

Let X be a continuum. For any positive integer n we consider the hyperspace Fn(X) and if n is greater than or equal to two, we consider the quotient space SFn(X) defined in [3]. For a given map f:X → X, we consider the induced maps Fn(f): Fn(X) → Fn(X) and SFn(f): SFn(X) → SFn(X) defined in [4]. Let M be one of the following classes of maps: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, minimal, irreducible, feebly open and turbulent. In this paper we study the relationships between the following statements: f M, Fn(f) M and SFn(f) M.

Keywords

Chaotic map, exact map; feebly open map; hyperspace; induced map; irreducible map; minimal map; mixing map; strongly transitive map; symmetric product; symmetric product suspension; totally transitive map; transitive map; turbulent map; weakly mixing map

Hrčak ID:

170048

URI

https://hrcak.srce.hr/170048

Publication date:

3.12.2016.

Visits: 995 *