Finite Invariant Sets with Bridging Points in Logistic IFS
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913032444051456 |
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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 |
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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 |