• Corpus ID: 240419739

Evolution to symmetry

  title={Evolution to symmetry},
  author={Ferdinand Verhulst},
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and ω > 0. The time-dependence produces slow evolution to discrete (mirror) symmetry in one of the degrees-of-freedom. This changes the dynamics drastically depending on the frequency ratio ω and the timescale of evolution. We analyse the cases ω = 1, 2, 3 where… 
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