Geodesic
Relatively unstable attractors
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 91-100.

Voir la notice de l'article provenant de la source Math-Net.Ru

There are different non-equivalent definitions of attractors in the theory of dynamical systems. The most common are two definitions: the maximal attractor and the Milnor attractor. The maximal attractor is by definition Lyapunov stable, but it is often in some ways excessive. The definition of Milnor attractor is more realistic from the physical point of view. The Milnor attractor can be Lyapunov unstable though. One of the central problems in the theory of dynamical systems is the question of how typical such a phenomenon is. This article is motivated by this question and contains new examples of so-called relatively unstable Milnor attractors. Recently I. Shilin has proved that these attractors are Lyapunov stable in the case of one-dimensional fiber under some additional assumptions. However, the question of their stability in the case of multidimensional fiber is still an open problem. 
@article{TM_2012_277_a6,
     author = {Yu. S. Ilyashenko and I. S. Shilin},
     title = {Relatively unstable attractors},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {91--100},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_277_a6/}
}
TY  - JOUR
AU  - Yu. S. Ilyashenko
AU  - I. S. Shilin
TI  - Relatively unstable attractors
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2012
SP  - 91
EP  - 100
VL  - 277
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2012_277_a6/
LA  - ru
ID  - TM_2012_277_a6
ER  - 
%0 Journal Article
%A Yu. S. Ilyashenko
%A I. S. Shilin
%T Relatively unstable attractors
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2012
%P 91-100
%V 277
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2012_277_a6/
%G ru
%F TM_2012_277_a6
Yu. S. Ilyashenko; I. S. Shilin. Relatively unstable attractors. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 91-100. http://geodesic.mathdoc.fr/item/TM_2012_277_a6/

[1] Hutchinson J., “Fractals and self similarity”, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR | Zbl

[2] Kudryashov Yu.G., “Kostistye attraktory”, Funkts. analiz i ego pril., 44:3 (2010), 73–76 | DOI | MR | Zbl