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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 051, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.051 (Mi sigma177) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System

Francesco Fassò, Andrea Giacobbe

Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35131 Padova, Italy
Full-text PDF (400 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2007.051
Abstract: Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We apply the result to the nonholonomic system of a ball rolling on a surface of revolution.
Keywords: systems with symmetry; reconstruction; integrable systems; nonholonomic systems.
Received: November 20, 2006; in final form March 15, 2007; Published online March 22, 2007
Bibliographic databases:
Document Type: Article
MSC: 37J35; 70H33
Language: English
Citation: Francesco Fassò, Andrea Giacobbe, “Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System”, SIGMA, 3 (2007), 051, 12 pp.
Citation in format AMSBIB
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\paper Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a~Nonholonomic
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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