An inequality in real Milnor-Thurston monotonicity problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913625387565056 |
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| author | Li, Ziyu Lu, Minyu Wang, Tianyu |
| author_facet | Li, Ziyu Lu, Minyu Wang, Tianyu |
| contents | In late 1990's Tsujii proved monotonicity of topological entropy of real quadratic family $f_c(x)=x^2+c$ on parameter $c$ by proving an inequality concerning orbital information of the critical point. In this paper, we consider a weak analog of such inequality for the general family $f_{c,r}(x)=|x|^r+c$ with rational $r>1$, by following an algebraic approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An inequality in real Milnor-Thurston monotonicity problem Li, Ziyu Lu, Minyu Wang, Tianyu Dynamical Systems In late 1990's Tsujii proved monotonicity of topological entropy of real quadratic family $f_c(x)=x^2+c$ on parameter $c$ by proving an inequality concerning orbital information of the critical point. In this paper, we consider a weak analog of such inequality for the general family $f_{c,r}(x)=|x|^r+c$ with rational $r>1$, by following an algebraic approach. |
| title | An inequality in real Milnor-Thurston monotonicity problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.18520 |