Invariant idempotent $\ast$-measures for generalized iterated function systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910093647282176 |
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| author | Mazurenko, Natalia Zarichnyi, Mykhailo |
| author_facet | Mazurenko, Natalia Zarichnyi, Mykhailo |
| contents | The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and establishes existence and uniqueness of invariant measures.
In the previous paper, IFSs of $\ast$-measures were considered. In the present paper we deal with generalized invariant function systems (GIFSs) of $\ast$-measures, which are counterparts of GIFSs in the sense of Mihail and Miculescu. The notion of invariant $\ast$-measure is introduced for such GIFSs and we prove existence and uniqueness of such elements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant idempotent $\ast$-measures for generalized iterated function systems Mazurenko, Natalia Zarichnyi, Mykhailo General Topology Dynamical Systems 28A80, 28A33, 54B20, 54B30 The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and establishes existence and uniqueness of invariant measures. In the previous paper, IFSs of $\ast$-measures were considered. In the present paper we deal with generalized invariant function systems (GIFSs) of $\ast$-measures, which are counterparts of GIFSs in the sense of Mihail and Miculescu. The notion of invariant $\ast$-measure is introduced for such GIFSs and we prove existence and uniqueness of such elements. |
| title | Invariant idempotent $\ast$-measures for generalized iterated function systems |
| topic | General Topology Dynamical Systems 28A80, 28A33, 54B20, 54B30 |
| url | https://arxiv.org/abs/2604.00663 |