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Monotonicity of entropy for real multimodal maps
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Bruin, H. and Strien, Sebastian van (2015) Monotonicity of entropy for real multimodal maps. Journal of the American Mathematical Society, Volume 28 . pp. 1-61. doi:10.1090/S0894-0347-2014-00795-5 ISSN 1088-6834.
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Abstract
In 1992, Milnor [28] posed the Monotonicity Conjecture that within a
family of real multimodal polynomial interval maps with only real critical points,
the isentropes, i.e., the sets of parameters for which the topological entropy is
constant, are connected. This conjecture was already proved in the mid-1980s for
quadratic maps by a number of different methods, see [30, 10, 9, 26, 42]. In 2000,
Milnor & Tresser [31], provided a proof for the case of cubic maps. In this paper
we will prove the general case of this 20 year old conjecture.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 1088-6834 | ||||
Official Date: | 2015 | ||||
Dates: |
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Volume: | Volume 28 | ||||
Page Range: | pp. 1-61 | ||||
DOI: | 10.1090/S0894-0347-2014-00795-5 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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