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UFN, 2010, Volume 180, Number 12, Pages 1305–1329 (Mi ufn2302)  

This article is cited in 31 scientific papers (total in 33 papers)


Fascination of chaos

A. Yu. Loskutov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories, homoclinic tangencies, wild hyperbolic sets and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodictheory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes by the investigation of the possibility to study complex systems on the basis of the analysis of registered signals, i.e. the generated time series.


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English version:
Physics–Uspekhi, 2010, 53:12, 1257–1280

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PACS: 02.50.-r, 05.45.-a, 47.52.+j
Received: May 17, 2010
Revised: August 5, 2010

Citation: A. Yu. Loskutov, “Fascination of chaos”, UFN, 180:12 (2010), 1305–1329; Phys. Usp., 53:12 (2010), 1257–1280

Citation in format AMSBIB
\by A.~Yu.~Loskutov
\paper Fascination of chaos
\jour UFN
\yr 2010
\vol 180
\issue 12
\pages 1305--1329
\jour Phys. Usp.
\yr 2010
\vol 53
\issue 12
\pages 1257--1280

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    2. L I Proverbio, E Lazzaro, S Ratynskaia, C Castaldo, U de Angelis, G Grosso, M De Angeli, “The dynamics of ferromagnetic dust particles in the FTU tokamak”, Plasma Phys. Control. Fusion, 53:11 (2011), 115013  crossref  adsnasa  isi  elib  scopus
    3. Kuznetsov S.P., “Skhemy elektronnykh ustroistv s giperbolicheskim khaosom i modelirovanie ikh dinamiki v programmnoi srede multisim”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 19:5 (2011), 98–115  zmath  elib
    4. N. I. Vaganova, E. N. Rumanov, “Critical chaos”, Dokl. Phys., 56:10 (2011), 507  crossref  zmath  adsnasa  isi  elib  elib  scopus
    5. A. Yu. Loskutov, A. V. Popkova, “Stabilization of chaotic oscillations in systems with a hyperbolic-type attractor”, JETP Letters, 94:1 (2011), 86–90  mathnet  crossref  isi
    6. A. V. Makarenko, “Structure of synchronized chaos studied by symbolic analysis in velocity-curvature space”, Tech. Phys. Lett, 38:2 (2012), 155  crossref  mathscinet  adsnasa  isi  elib  scopus
    7. A. V. Makarenko, “Measure of synchronism of multidimensional chaotic sequences based on their symbolic representation in a T-alphabet”, Tech. Phys. Lett, 38:9 (2012), 804  crossref  adsnasa  isi  elib  scopus
    8. Olga B. Isaeva, Sergey P. Kuznetsov, Igor R. Sataev, “A “saddle-node” bifurcation scenario for birth or destruction of a Smale–Williams solenoid”, Chaos, 22:4 (2012), 043111  crossref  mathscinet  zmath  isi  scopus
    9. Kuznetsov A.S., “Parametricheskie generatory s khaoticheskoi amplitudnoi dinamikoi, otvechayuschei attraktoram tipa smeila-vilyamsa”, Izvestiya vysshikh uchebnykh zavedenii. prikladnaya nelineinaya dinamika, 20:1 (2012), 129–136  mathscinet  zmath  elib
    10. Vyatkin V.B., “Sinergeticheskaya teoriya informatsii: poyasneniya i terminologicheskie zamechaniya”, Politematicheskii setevoi elektronnyi nauchnyi zhurnal kubanskogo gosudarstvennogo agrarnogo universiteta, 2012, no. 80, 11–46  elib
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