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Regular and Chaotic Dynamics

, Volume 17, Issue 3–4, pp 273–292 | Cite as

Normal form construction for nearly-integrable systems with dissipation

  • Aessandra CellettiEmail author
  • Christoph Lhotka
Article

Abstract

We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a dissipative contribution is added. The vector field depends upon two parameters, namely the perturbing and dissipative parameters, and by a drift term. We study an -dimensional, time-dependent vector field, which is motivated by mathematical models in Celestial Mechanics. Assuming to start with non-resonant initial conditions, we provide the construction of the normal form up to an arbitrary order. To construct the normal form, a suitable choice of the drift parameter must be performed. The normal form allows also to provide an explicit expression of the frequency associated to the normalized coordinates. We also give an example in which we construct explicitly the normal form, we make a comparison with a numerical integration, and we determine the parameter values and the time interval of validity of the normal form.

Keywords

dissipative system normal form non-resonant motion 

MSC2010 numbers

37J35 

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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly
  2. 2.Namur Center for Complex Systems, Départment de MathématiqueUniversité FUNDPNamurBelgium

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