Glasnik Matematicki, Vol. 51, No. 2 (2016), 453-474.

DYNAMIC PROPERTIES FOR THE INDUCED MAPS ON n-FOLD SYMMETRIC PRODUCT SUSPENSIONS

Franco Barragán, Alicia Santiago-Santos and 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
e-mail: franco@mixteco.utm.mx
e-mail: alicia@mixteco.utm.mx
e-mail: jtenorio@mixteco.utm.mx

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.

2010 Mathematics Subject Classification.   54B20, 37B45, 54F50, 54F15.

Key words and phrases.   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.


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DOI: 10.3336/gm.51.2.12


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