Using SFT techniques, Eliashberg et al. (Geom Topol 10:1635–1747, 2006) proved that if \(\pi R_2^2 \le K \le \pi R_1^2\) for some integer K, then there is no contact squeezing in \({\mathbb {R}}^{2n} \times S^1\) of the prequantization of the ball of radius \(R_1\) into the prequantization of the ball of radius \(R_2\) . This result was extended to the case of balls of radius \(R_1\) and \(R_2\) with \(1 \le \pi R_2^2 \le \pi R_1^2\) by Chiu (Duke Math J 166:605–655, 2017) and the first author (Int J Math 27:1650107, 2016), using, respectively, microlocal sheaves and SFT. In the present article we recover this general contact non-squeezing theorem using generating functions, a classical method based on finite dimensional Morse theory. More precisely, we develop an equivariant version, with respect to a certain action of a finite cyclic group, of the generating function homology for domains of \({\mathbb {R}}^{2n} \times S^1\) defined by the second author (Ann Inst Fourier (Grenoble) 61:145–185, 2011). A key role in the construction is played by translated chains of contactomorphisms, a generalization of translated points.
