Finite Invariant Sets with Bridging Points in Logistic IFS

Fuente: arXiv
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Main Authors: Kato, Hibiki, Onozaki, Tamotsu, Saiki, Yoshitaka, Sugita, Yasumasa
Format: Preprint
Published: 2026
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author Kato, Hibiki
Onozaki, Tamotsu
Saiki, Yoshitaka
Sugita, Yasumasa
author_facet Kato, Hibiki
Onozaki, Tamotsu
Saiki, Yoshitaka
Sugita, Yasumasa
contents We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate between fixed points and periodic orbits of the constituent maps. We derive exact parameter conditions for several toss-and-catch structures in a pair of logistic maps (logistic IFS) and a combination of logistic and tent maps (logistic-tent IFS). Notably, we identify cases in which the invariant set contains bridging points that belong to neither of the invariant sets of the individual maps.
format Preprint
id arxiv_https___arxiv_org_abs_2604_13124
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Finite Invariant Sets with Bridging Points in Logistic IFS
Kato, Hibiki
Onozaki, Tamotsu
Saiki, Yoshitaka
Sugita, Yasumasa
Dynamical Systems
Chaotic Dynamics
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate between fixed points and periodic orbits of the constituent maps. We derive exact parameter conditions for several toss-and-catch structures in a pair of logistic maps (logistic IFS) and a combination of logistic and tent maps (logistic-tent IFS). Notably, we identify cases in which the invariant set contains bridging points that belong to neither of the invariant sets of the individual maps.
title Finite Invariant Sets with Bridging Points in Logistic IFS
topic Dynamical Systems
Chaotic Dynamics
url https://arxiv.org/abs/2604.13124