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

Dynamics of induced mappings on symmetric products, some answers

“…( [5,Theorem 4.1] it was shown that each one of the statements (2), ( 3) and ( 4) implies (1). The authors of [4] and [5] supposed that the spaces are continua, however, it is easy see that the proofs for these results are valid for infinite compact metric spaces without isolated points. The rest of the implications among (1), ( 2), ( 3) and ( 4) are left as questions in [4, Questions 5.5] and [5,Question 4.2].…”

“…The authors of [4] and [5] supposed that the spaces are continua, however, it is easy see that the proofs for these results are valid for infinite compact metric spaces without isolated points. The rest of the implications among (1), ( 2), ( 3) and ( 4) are left as questions in [4, Questions 5.5] and [5,Question 4.2]. The purpose of this section is to complete the proof that, in fact, all the statements (1)-( 4) are equivalent.…”

“…Of course, this problem has also been considered for other hyperspaces. Dynamical properties of induced mappings on symmetric products have been considered in [2], [3], [4], [5], [6], [9], [10], [11] and [14]. In particular, in [4] and [5], the properties of being: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, minimal, irreducible, feebly open and turbulent were studied.…”

“…The aim of this paper is to solve most of the problems posed by F. Barragán, A. Santiago-Santos and J. Tenorio in [4] and [5], related to the properties: minimality, irreducibility, strong transitivity and turbulence.…”

Compacto transitividad y su relación con tipos de sensitividad

“…De manera abstracta, un sistema dinámico discreto será una pareja (X, f ), donde X es un espacio métrico compacto, conexo con más de un elemento y f : X → X es una función continua y suprayectiva. En la actualidad, se han desarrollado algunas publicaciones, por mencionar, vea por ejemplo [3,4,5,15].…”