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Domagoj Jelić

Publications and source records attributed to Domagoj Jelić.

3 recordsLinked to original sources
arXiv2026

Special $α$-limit sets in the hyperspace of continua: closedness and entropy for interval maps

This paper investigates the backward dynamics of hyperspace systems induced by continuous interval maps. Focusing on the hyperspace of continua, we provide a structural characterization of the $α$-limit sets of backward branches for interval subcontinua. A central result of this work is the proof that the special $α$-limit set of any nondegenerate subinterval is always closed. This reveals a striking topological contrast with classical single-point dynamics, where special $α$-limit sets need not be closed. Finally, we prove that if a special $α$-limit set contains two nondegenerate periodic continua with disjoint orbits, then the base map has a horseshoe and, consequently, positive topological entropy.

math.DS↗
arXiv2026

On limit sets and equicontinuity in the hyperspace of continua in dimension one

The paper studies the structure of $ω$-limit sets of map $\tilde{f}$ induced on the hyperspace $C(G)$ of all connected compact sets, by dynamical system $(G,f)$ acting on a topological graph $G$. In the case of the base space being a topological tree we additionally show that $\tilde{f}$ is always almost equicontinuous and characterize its Birkhoff center.

math.DS↗
arXiv2025

On recurrence and entropy in hyperspace of continua in dimension one

We show that if $G$ is a topological graph, and $f$ is continuous map, then the induced map $\tilde{f}$ acting on the hyperspace $C(G)$ of all connected subsets of $G$ by natural formula $\tilde{f}(C)=f(C)$ carries the same entropy as $f$. This is well known that it does not hold on the larger hyperspace of all compact subsets. Also negative examples were given for the hyperspace $C(X)$ on some continua $X$, including dendrites. Our work extends previous positive results obtained first for much simpler case of compact interval by completely different tools.

math.DS↗