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Monotonicity of the Period Function of the Liénard Equation of Second Kind

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Abstract

This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Liénard II type equation given by \({\ddot{x}} + f(x){\dot{x}}^{2} + g(x) = 0\). We generalize Chicone’s result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.

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Acknowledgements

We would like to thank Professor Carmen Chicone, Professor Peter Leach and Professor Jean-Marie Strelcyn for their help and valuable comments in the preparation of the manuscript. We would also like to thank Mr. Ankan Pandey for computational assistance. Finally we thank the anonymous reviewer for his careful reading of our manuscript and his many insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta, 700009, India

    A. Ghose-Choudhury

  2. SN Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India

    Partha Guha

Authors
  1. A. Ghose-Choudhury
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  2. Partha Guha
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Correspondence to Partha Guha.

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Dedicated to our friend Carmen Chicone on his 70th birthday with great respect and admiration.

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Ghose-Choudhury, A., Guha, P. Monotonicity of the Period Function of the Liénard Equation of Second Kind. Qual. Theory Dyn. Syst. 16, 609–621 (2017). https://doi.org/10.1007/s12346-017-0227-2

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  • DOI: https://doi.org/10.1007/s12346-017-0227-2

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