Description of fixed points of an infinite dimensional operator
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912149405696000 |
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| author | Umrbek, Olimov |
| author_facet | Umrbek, Olimov |
| contents | We consider an infinite-dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values. It is known that finding the fixed points of an infinite-dimensional operator is generally impossible. But we have fully analyzed the fixed points of an infinite-dimensional operator by applying a technique of reducing an infinite-dimensional operator to a two-dimensional operator. The set of parameters is divided into subsets $A_{i,j},$ where the index $i$ means the number of fixed points on the line $y=x$, $j$ means the number of fixed points outside of $y=x.$ The number of fixed points can be up to seven, and the explicit form of each fixed point is found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Description of fixed points of an infinite dimensional operator Umrbek, Olimov Dynamical Systems We consider an infinite-dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values. It is known that finding the fixed points of an infinite-dimensional operator is generally impossible. But we have fully analyzed the fixed points of an infinite-dimensional operator by applying a technique of reducing an infinite-dimensional operator to a two-dimensional operator. The set of parameters is divided into subsets $A_{i,j},$ where the index $i$ means the number of fixed points on the line $y=x$, $j$ means the number of fixed points outside of $y=x.$ The number of fixed points can be up to seven, and the explicit form of each fixed point is found. |
| title | Description of fixed points of an infinite dimensional operator |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.06443 |