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- W763311492 abstract "We study the existence of families of periodic solutions in a neighbourhood of a symmetric equilibrium point in two classes of Hamiltonian systems with involutory symmetry. In both classes, the involution reverses the sign of the Hamiltonian function, and the system is in 1:1 resonance. In the first class we study a Hamiltonian system with a reversing involution R acting symplectically. We first recover a result of Buzzi and Lamb showing that the equilibrium point is contained in a three dimensional conical subspace which consists of a two parameter family of periodic solutions with symmetry R, and furthermore that there may or may not exist two families of non-symmetric periodic solutions, depending on the coefficients of the Hamiltonian (correcting a minor error in their paper). In the second problem we study an equivariant Hamiltonian system with a symmetry S that acts anti-symplectically. Generically, there is no S-symmetric solution in a neighbourhood of the equilibrium point. Moreover, we prove the existence of at least 2 and at most 12 families of non-symmetric periodic solutions. We conclude with a brief study of systems with both forms of symmetry, showing they have very similar structure to the system with symmetry R." @default.
- W763311492 created "2016-06-24" @default.
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- W763311492 date "2016-02-08" @default.
- W763311492 modified "2023-09-27" @default.
- W763311492 title "Periodic Orbits in Hamiltonian Systems with Involutory Symmetries" @default.
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- W763311492 doi "https://doi.org/10.1007/s10884-016-9519-5" @default.
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