Note on the metric entropy for multivalued maps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909230261338112 |
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| author | Andres, Jan Ludvík, Pavel |
| author_facet | Andres, Jan Ludvík, Pavel |
| contents | The main aim of this note is to point out by means of counter-examples that some arguments of the proofs of two theorems about a "half variational principle" for multivalued maps, formulated recently by Vivas and Sirvent [Metric entropy for set-valued maps, Discrete Contin. Dyn. Syst. Ser. B, 27 (2022), pp. 6589-6604], are false and that our corrected versions require rather restrictive additional assumptions. Nevertheless, we will be able to establish the full variational principle for a special subclass of multivalued lower semicontinuous maps with convex compact values on a compact subset of a Banach space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16579 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on the metric entropy for multivalued maps Andres, Jan Ludvík, Pavel Dynamical Systems 28D20, 37B40, 54C60 The main aim of this note is to point out by means of counter-examples that some arguments of the proofs of two theorems about a "half variational principle" for multivalued maps, formulated recently by Vivas and Sirvent [Metric entropy for set-valued maps, Discrete Contin. Dyn. Syst. Ser. B, 27 (2022), pp. 6589-6604], are false and that our corrected versions require rather restrictive additional assumptions. Nevertheless, we will be able to establish the full variational principle for a special subclass of multivalued lower semicontinuous maps with convex compact values on a compact subset of a Banach space. |
| title | Note on the metric entropy for multivalued maps |
| topic | Dynamical Systems 28D20, 37B40, 54C60 |
| url | https://arxiv.org/abs/2406.16579 |