抄録
Poincar ́e map is a general tool to treat limit cycles in dynamical systems. In or- der to prove existence of a limit cycle by validated computation, Zgliczyn ́ski ver- ified existence of a fixed point of a Poincar ́e map using a fixed point theorem[5]. However it was not an easy work to specify ’first return time’ Ts, a time period between an initial point x0 on the Poincar ́e section Γ and x1 := φ(Ts, x0) ∈ Γ, where φ(t, x0) denotes a point on the trajectory from x0 at time t. Of course one have to verify that there is no point φ(t, x0) ∈ Γ for any t ∈ (0, Ts). Zgliczyn ́ski proposed a way to handle the situation and showed numerical examples to ap- peal effectiveness of his method.
Hereafter we propose another way in which one has not to construct a Poincar ́e map any longer.