In this paper, we prove first that the space of minimal sets of any homeomorphisms $ f: X\to X
$ of a regular curve $ X $ is closed in the hyperspace $2^ X $ of closed subsets of $ X …

In the paper we study what sets can be obtained as $\alpha $-limit sets of backward
trajectories in graph maps. We show that in the case of mixing maps, all those $\alpha $-limit …

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be
completely invariant. This highlights unexpected dynamical behavior in these maps …

Abstract Let f: X→ X be a continuous map on a compact metric space X and let α f, ω f and
ICT f denote the set of α-limit sets, ω-limit sets and nonempty closed internally chain …

Special α-limit sets (sα-limit sets) combine together all accumulation points of all backward
orbit branches of a point x under a noninvertible map. The most important question about …

We investigate the notion of the special α-limit set of a point. For a continuous selfmap of a
compact metric space, it is defined as the union of the sets of accumulation points over all …

If X is a local dendrite and f: X→ X is a continuous map without periodic points then we prove
that the canonical graph (the minimal subcontinuum containing all simple closed curves) …

Many phenomena coming from the biology, economy, engineering are modeled using
discrete dynamical systems. The concept of backward orbit is an essential concept for …

We consider the complexity of special-limit sets, a kind of backward limit set for non-
invertible dynamical systems. We show that these sets are always analytic, but not …

Let $ X $ be a regular curve and let $ f: X\to X $ be a monotone map. In this paper,
nonwandering set of $ f $ and the structure of special $\alpha $-limit sets for $ f $ are …