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Research article

An example in Hamiltonian dynamics

  • Received: 11 November 2023 Revised: 03 April 2024 Accepted: 08 May 2024 Published: 11 June 2024
  • Primary 05C38, 15A15; Secondary 05A15, 15A18

  • We present an example of a three-degrees-of-freedom polynomial Hamilton function with a critical point characterized by indefinite quadratic part with a Morse index 2. This function generates a Hamiltonian system wherein all eigenvalues equal ±i, but it lacks small-amplitude periodic solutions with a period 2π.

    Citation: Henryk Żoła̧dek. An example in Hamiltonian dynamics[J]. Communications in Analysis and Mechanics, 2024, 16(2): 431-447. doi: 10.3934/cam.2024020

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  • We present an example of a three-degrees-of-freedom polynomial Hamilton function with a critical point characterized by indefinite quadratic part with a Morse index 2. This function generates a Hamiltonian system wherein all eigenvalues equal ±i, but it lacks small-amplitude periodic solutions with a period 2π.





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