Degenerate branching points of autonomous Hamiltonian systems Original Research Article

This paper deals with non-constant 2π-periodic solutions of View the MathML source where λ∈(0,+∞) and View the MathML source with View the MathML source for x0∈(∇H)−1({0}). Sufficient conditions for the existence of connected branches of such solutions bifurcating from (x0,λ0) have been formulated. The corresponding theorem concerning connected branches of arbitrary periodic nonstationary trajectories of the Hamiltonian system View the MathML source emanating from x0 has been proved. Minimal periods of trajectories near x0 have been described