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Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems

  • Adriana BuicăEmail author
  • Isaac A. García
  • Susanna Maza
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)

Abstract

In this paper we show novel applications of the inverse Jacobi multiplier focusing on questions of bifurcations and existence of periodic solutions admitted by both autonomous and non-autonomous systems of ordinary differential equations. In the autonomous case we focus on dimension n ≥ 3 whereas in the non-autonomous we study the cases with n ≥ 2. We summarize results already published and additionally we state some recent results to appear. The principal object of this research is two fold: first to prove the existence and smoothness of inverse Jacobi multiplier V in the region of interest in the phase space and second to show that the invariant set under the flow given by the zero-set of an inverse Jacobi multiplier contains under some assumptions orbits which are relevant in its phase portrait such as periodic orbits, limit cycles, stable, unstable and center manifolds and so on. In the non-autonomous T-periodic case we show some relationships between T-periodic orbits and T-periodic inverse Jacobi multipliers.

Keywords

Vector Field Periodic Orbit Center Manifold Infinitesimal Generator Linear Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Adriana Buică
    • 1
    Email author
  • Isaac A. García
    • 2
  • Susanna Maza
    • 2
  1. 1.Department of Applied MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Departament de MatemàticaUniversitat de LleidaLleidaSpain

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