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{Turaev:2015:10.1007/s00220-015-2338-4,
author = {Turaev, D},
doi = {10.1007/s00220-015-2338-4},
journal = {Communications in Mathematical Physics},
pages = {1235--1277},
title = {Maps close to identity and universal maps in the newhouse domain},
url = {http://dx.doi.org/10.1007/s00220-015-2338-4},
volume = {335},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Given an n-dimensional C r-diffeomorphism g, its renormalized iteration is an iteration of g, restricted to a certain n-dimensional ball and taken in some C r-coordinates in which the ball acquires radius 1. We show that for any r ≥ 1 the renormalized iterations of C r-close to identity maps of an n-dimensional unit ball B n (n ≥ 2) form a residual set among all orientation-preserving C r-diffeomorphisms B n→ R n. In other words, any generic n-dimensional dynamical phenomenon can be obtained by iterations of C r-close to identity maps, with the same dimension of the phase space. As an application, we show that any C r-generic two-dimensional map that belongs to the Newhouse domain (i.e., it has a so-called wild hyperbolic set, so it is not uniformly-hyperbolic, nor uniformly partially-hyperbolic) and that neither contracts, nor expands areas, is C r-universal in the sense that its iterations, after an appropriate coordinate transformation, C r-approximate every orientation-preserving two-dimensional diffeomorphism arbitrarily well. In particular, every such universal map has an infinite set of coexisting hyperbolic attractors and repellers.
AU  - Turaev,D
DO  - 10.1007/s00220-015-2338-4
EP  - 1277
PY  - 2015///
SN  - 0010-3616
SP  - 1235
TI  - Maps close to identity and universal maps in the newhouse domain
T2  - Communications in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s00220-015-2338-4
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000351224000008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00220-015-2338-4
UR  - http://hdl.handle.net/10044/1/53372
VL  - 335
ER  -
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