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- W2267273314 abstract "Publisher Summary This chapter describes the periodic and nonperiodic solutions of reversible systems. It discusses the recent results about the existence of bounded solutions for finite systems of ordinary differential equations, which are reversible in the sense of G.D. Birkhoff . These solutions appear under various conditions when, for some value of an external parameter, an equilibrium point exhibits bifurcation. For the case n = 2, the local and global existence of periodic solutions has been proved by Wolkowisky, the global aspects depending strongly on the validity of nodal properties and the restriction to two dimensions. The extension of the local bifurcation result to arbitrary dimensions is straightforward if one follows the general lines of theorem. However, the global result is by no means trivial. Using a new uniqueness result, global existence of periodic solutions for arbitrary dimensions could be established. A particularly deep existence problem arises when A has k pairs of single eigenvalues on the imaginary axis. As related questions for Hamiltonian systems indicate, one external parameter generally does not suffice to make the bifurcation of the expected quasiperiodic solutions." @default.
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- W2267273314 date "1981-01-01" @default.
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- W2267273314 title "PERIODIC AND NONPERIODIC SOLUTIONS OF REVERSIBLE SYSTEMS" @default.
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- W2267273314 doi "https://doi.org/10.1016/b978-0-12-508780-3.50024-9" @default.
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