3 citations · 17 across the 17 of their papers we have counts for
18 papers
Retract or Not: A Tale of Two Fans
Iztok Banic, Goran Erceg, Sina Greenwood +1
Let be a Lelek fan or a Cantor fan and let be a Lelek fan or a Cantor fan. In this paper, we study embeddings that admit retractions from onto .…
Specification in Mahavier Systems via Closed Relations
Iztok Banič, Goran Erceg, Ivan Jelić +1
We study two fundamental properties of topological dynamical systems, the specification property and the initial specification property, and explore their generalizations to the br…
Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps
Iztok Banic, Goran Erceg, Ivan Jelic +1
The Lelek fan is the only smooth fan that has a dense set of end-points. In this paper, we study non-smooth fans with this property; i.e., we construct an uncountable family of pai…
Chaos and mixing homeomorphisms on fans
Iztok Banic, Goran Erceg, Judy Kennedy +2
We construct a mixing homeomorphism on the Lelek fan. We also construct a mixing homeomorphism on the Cantor fan. Then, we construct a family of uncountably many pairwise non-homeo…
An uncountable family of non-smooth fans that admit transitive homeomorphisms
Iztok Banic, Judy Kennedy, Chris Mouron +1
Recently, many examples of smooth fans that admit a transitive homeomorphism have been constructed. For example, a family of uncountably many pairwise non-homeomorphic smooth fans…
Quotients of dynamical systems and chaos on the Cantor fan
Iztok Banic, Goran Erceg, Judy Kennedy +1
Let be a dynamical system. Using an equivalence relation on , we introduce the quotient of the dynamical system . In the first part…
An uncountable family of smooth fans that admit transitive homeomorphisms
Iztok Banic, Goran Erceg, Judy Kennedy +2
We construct a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms. In addition, we show that the star of Cantor fans admits a tra…
An embedding of the Cantor fan into the Lelek fan
Iztok Banič, Goran Erceg, Judy Kennedy
The Lelek fan is usually constructed as a subcontinuum of the Cantor fan in such a way that the set of the end-points of is dense in . It easily follows that the Lelek f…
Transitive mappings on the Cantor fan
Iztok Banič, Goran Erceg, Judy Kennedy +2
Many continua that admit a transitive homeomorphism may be found in the literature. The circle is probably the simplest non-degenerate continuum that admits such a homeomorphism. O…
A transitive homeomorphism on the Lelek fan
Iztok Banič, Goran Erceg, Judy Kennedy
Let be a continuum and let be a homeomorphism. To construct a dynamical system with interesting dynamical properties, the continuum often needs t…
Sufficient conditions for non-zero entropy and finite relations
Iztok Banic, Rene Gril Rogina, Judy Kennedy +1
We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient condition…
The Lelek fan as the inverse limit of intervals with a single set-valued bonding function whose graph is an arc
Iztok Banic, Goran Erceg, Judy Kennedy
We consider a family of inverse limits of inverse sequences of closed unit intervals with a single upper semi-continuous set-valued bonding function whose graph is an arc; it is th…
Minimal dynamical systems with closed relations
Iztok Banic, Goran Erceg, Rene Gril Rogina +1
We introduce dynamical systems with closed relations on compact metric spaces and discuss different types of minimality of such dynamical systems, all of them gener…
Closed relations with non-zero entropy that generate no periodic points
Iztok Banic, Goran Erceg, Judy Kennedy
The paper is motivated by E. Akin's book about dynamical systems and closed relations [A], and by J. Kennedy's and G. Erceg's recent paper about the entropy of closed relations on…
Mapping and fixed point property theorems for inverse limits with set-valued bonding functions
Iztok Banic, Goran Erceg, Judy Kennedy
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicont…
Span of a Graph: Keeping the Safety Distance
Iztok Banič, Andrej Taranenko
Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we sol…
Characterizations of -like continua that do not have the fixed point property
Iztok Banic, Judy Kennedy, Piotr Minc
We give two characterizations of -like continua that do not have the fixed point property. Both characterizations are stated in terms of sequences of open covers of…
Integrations on rings
Iztok Banic
In calculus, an indefinite integral of a function is a differentiable function whose derivative is equal to . In present paper, we generalize this notion of the indefini…