Conceptions on topological transitivity in products and symmetric products

Authors

ANAHI ROJAS
FRANCO BARRAGAN
SERGIO MACÍAS

DOI

10.3906/mat-1912-67

Abstract

Having a finite number of topological spaces $X_i$ and functions $f_i : X_i \to X_i$, and considering one of the following classes of functions: exact, transitive, strongly transitive, totally transitive, orbit-transitive, strictly orbittransitive, $\omega$-transitive, mixing, weakly mixing, mild mixing, chaotic, exactly Devaney chaotic, minimal, backward minimal, totally minimal, $TT_{++}$, scattering, Touhey or an $F$ -system, in this paper, we study dynamical behaviors of the systems $(X_i,f_i)$, $(\prod X_i,\prod f_i)$, $(\mathcal{F}_n(\prod X_i),\mathcal{F}_n(\prod f_i))$, and $(\mathcal{F}_n(X_i),\mathcal{F}_n(f_i))$.

Keywords

Topological transitivity, symmetric products, dynamical systems

First Page

491

Last Page

523

Recommended Citation

ROJAS, ANAHI; BARRAGAN, FRANCO; and MACÍAS, SERGIO (2020) "Conceptions on topological transitivity in products and symmetric products," Turkish Journal of Mathematics: Vol. 44: No. 2, Article 12. https://doi.org/10.3906/mat-1912-67
Available at: https://journals.tubitak.gov.tr/math/vol44/iss2/12