On the dynamics of a kicked harmonic oscillator

  • J. M. TuwankottaEmail author
  • A. F. Ihsan


In this paper the dynamics of a kicked harmonic oscillator is studied. This is done by constructing a stroboscopic map for the kicked harmonic oscillator by following the time t-flow of the differential equation and taking phase portrait for some integrals multiple of the period of the kicked. The resulting map is a two-dimensional area-preserving (or symplectic) map. We provide a proof for the continuity of the position, and also a local stability analysis for the trivial equilibrium. Complete analysis for a general kick function for the 1:1, and for the 1:2 resonances are presented. For the 1:4 resonance, we describe the dynamics numerically for some specific kick functions.


Area-preserving map Dynamics Resonance 



JMT thanks Prof. W.T. van Horssen (Technical University Delft, the Netherlands) , Prof. G.R.W. Quispel and Prof. P. H. van der Kamp (La Trobe University, Melbourne, Australia) for their hospitality during his visits to both universities during the execution of this research.


This research is supported by Riset P3MI 2017, Institut Teknologi Bandung, Indonesia.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Analysis and Geometry, FMIPAInstitut Teknologi BandungBandungIndonesia

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