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TMF, 2006, Volume 146, Number 3, Pages 447–466 (Mi tmf2047)  

This article is cited in 3 scientific papers (total in 3 papers)

The nature of the bufferness phenomenon in weakly dissipative systems

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We propose a mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one and a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipative, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of $RLC$ circuits in the feedback circuit.

Keywords: attractors, periodic motions, bufferness phenomenon, mappings, relay systems

DOI: https://doi.org/10.4213/tmf2047

Full text: PDF file (1058 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 376–392

Bibliographic databases:

Received: 11.11.2005
Revised: 16.06.2005

Citation: A. Yu. Kolesov, N. Kh. Rozov, “The nature of the bufferness phenomenon in weakly dissipative systems”, TMF, 146:3 (2006), 447–466; Theoret. and Math. Phys., 146:3 (2006), 376–392

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Resonance Dynamics of Nonlinear Flutter Systems”, Proc. Steklov Inst. Math., 261 (2008), 149–170  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Higuera M, Porter J, Knobloch E, “Faraday waves, streaming flow, and relaxation oscillations in nearly circular containers”, Chaos, 18:1 (2008), 015104  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. N. Kh. Rozov, “Fenomen bufernosti v matematicheskikh modelyakh estestvoznaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 3, 58–63  mathnet  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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