Monotonicity of entropy for real multimodal maps
File(s)
Accepted version
Author(s)
Bruin, H
van Strien, S
Type
Journal Article
Abstract
In 1992, Milnor 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 A. Douady (1993, 1995), A. Douady and J.H. Hubbard (1984, 1985), W. de Melo and S. van Strein (1993), J. Milnor and W. Thurston (1986, 1988), and M. Tsujii (2000). In 2000, Milnor and Tresser, provided a proof for the case of cubic maps. In this paper we will prove the general case of this 20 year old conjecture.
Date Issued
2015-01-01
Date Acceptance
2013-11-05
Citation
Journal of the American Mathematical Society, 2015, 28 (1), pp.1-61
ISSN
0894-0347
Publisher
American Mathematical Society
Start Page
1
End Page
61
Journal / Book Title
Journal of the American Mathematical Society
Volume
28
Issue
1
Copyright Statement
© 2014 American Mathematical Society. First published in Journal of the American Mathematical Society in vol. 28 (2015), published by the American Mathematical Society.
Identifier
http://arxiv.org/abs/0905.3377v2
Subjects
math.DS
math.DS
37E05, 37B40
Notes
Final version. To appear in Journal of the AMS
Publication Status
Published
Date Publish Online
2014-06-23