Imperial College London
Professor Dmitry Turaev

ProfessorDmitryTuraev

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics & Mathematical Physics
 
 
 
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Contact

 

d.turaev

 
 
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Location

 

634Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Asaoka:2017:10.1007/s00208-016-1468-0,
author = {Asaoka, M and Shinohara, K and Turaev, D},
doi = {10.1007/s00208-016-1468-0},
journal = {Mathematische Annalen},
pages = {1277--1309},
title = {Degenerate behavior in non-hyperbolic semigroup actions on the interval:  fast growth of periodic points and universal dynamics},
url = {http://dx.doi.org/10.1007/s00208-016-1468-0},
volume = {368},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider semigroup actions on the unit interval generated by strictlyincreasing $C^r$-maps. We assume that one of the generators has a pair of fixedpoints, one attracting and one repelling, and a heteroclinic orbit thatconnects the repeller and attractor, and the other generators form a robustblender, which can bring the points from a small neighborhood of the attractorto an arbitrarily small neighborhood of the repeller. This is a model settingfor partially hyperbolic systems with one central direction.  We show that, under additional conditions on the non-linearity and theSchwarzian derivative, the above semigroups exhibit, $C^r$-generically for anyr, arbitrarily fast growth of the number of periodic points as a function ofthe period. We also show that a $C^r$-generic semigroup from the class underconsideration supports an ultimately complicated behavior called universaldynamics.
AU  - Asaoka,M
AU  - Shinohara,K
AU  - Turaev,D
DO  - 10.1007/s00208-016-1468-0
EP  - 1309
PY  - 2017///
SN  - 0025-5831
SP  - 1277
TI  - Degenerate behavior in non-hyperbolic semigroup actions on the interval:  fast growth of periodic points and universal dynamics
T2  - Mathematische Annalen
UR  - http://dx.doi.org/10.1007/s00208-016-1468-0
UR  - http://hdl.handle.net/10044/1/41910
VL  - 368
ER  -
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