The time-dependent displacement or motion y(t,x) of an isentropic elastic material in one space dimension satisfies the second-order nonlinear equation
We give now the proof of Lemma 2.2. We mention that these estimates were done in  for dimensions N≥2 and in the particular case s=α using some technical results of . We provide here the proof for all s∈(0,2) and α∈(0,2) in the one-dimensiona…
Let (fλ)λ∈Λ be a holomorphic family of rational maps of degree d≥2 on P1 with dim(Λ)=m. Let ωΛ be a Kähler form on Λ. Assume that c1,…,ck are marked critical points and let T1,…,Tk be their respective bifurcation currents (see Section 2.1).
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