On the continuity of entropy of Lorenz maps
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866908760396529664 |
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| author | Cooperband, Zoe Pearse, Erin P. J. Quackenbush, Blaine Rowley, Jordan M. Samuel, Tony West, Matthew A. |
| author_facet | Cooperband, Zoe Pearse, Erin P. J. Quackenbush, Blaine Rowley, Jordan M. Samuel, Tony West, Matthew A. |
| contents | We consider a one parameter family of Lorenz maps indexed by their point of discontinuity $p$ and constructed from a pair of bilipschitz functions. We prove that their topological entropies vary continuously as a function of $p$ and discuss Milnor's monotonicity conjecture in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_04511 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the continuity of entropy of Lorenz maps Cooperband, Zoe Pearse, Erin P. J. Quackenbush, Blaine Rowley, Jordan M. Samuel, Tony West, Matthew A. Dynamical Systems 37B40, 37E05 (Primary), 37B10 (Secondary) We consider a one parameter family of Lorenz maps indexed by their point of discontinuity $p$ and constructed from a pair of bilipschitz functions. We prove that their topological entropies vary continuously as a function of $p$ and discuss Milnor's monotonicity conjecture in this setting. |
| title | On the continuity of entropy of Lorenz maps |
| topic | Dynamical Systems 37B40, 37E05 (Primary), 37B10 (Secondary) |
| url | https://arxiv.org/abs/1803.04511 |