For the cubic conformal wave equation on the Einstein cylinder, time-periodic solutions form complex trunk-branch bifurcation networks, and a resummed Poincaré-Lindstedt series is claimed to encode these structures.
Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$
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We prove existence and multiplicity of Cantor families of small amplitude analytic in time periodic solutions of the completely resonant cubic nonlinear Klein-Gordon equation on $\mathbb{S}^3$ for an asymptotically full measure set of frequencies close to 1. The solutions are constructed by a Lyapunov-Schmidt decomposition and a Nash-Moser iterative scheme. We first find non-degenerate solutions of the Kernel equation. Then we solve the Range equation with a Nash-Moser iterative scheme to overcome small divisors problems.
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Time-periodic solutions of the conformally invariant wave equation on the Einstein cylinder
For the cubic conformal wave equation on the Einstein cylinder, time-periodic solutions form complex trunk-branch bifurcation networks, and a resummed Poincaré-Lindstedt series is claimed to encode these structures.