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We measure the galaxy 2- and 3-point correlation functions at $z=[0.5,0.7]$and $z=[0.7, 0.9]$, from the final data release of the VIPERS survey (PDR2). Wemodel the two statistics including a nonlinear 1-loop model for the 2-pointfunction and a tree-level model for the 3-point function, and perform a jointlikelihood analysis. The entire process and nonlinear corrections are testedand validated through the use of the 153 highly realistic VIPERS mockcatalogues, showing that they are robust down to scales as small as 10 $h^{-1}\, \mathrm{Mpc}$. The mocks are also adopted to compute the covariance matrixthat we use for the joint 2- and 3-point analysis. Despite the limitedstatistics of the two (volume-limited) sub-samples analysed, we demonstratethat such a combination successfully breaks the degeneracy existing at 2-pointlevel between clustering amplitude $\sigma_8$, linear bias $b_1$ and the lineargrowth rate of fluctuations $f$. For the latter, in particular, we measure$f(z=0.61)=0.64^{+0.55}_{-0.37}$ and $f(z=0.8)=1.0\pm1.0$, while the amplitudeof clustering is found to be $\sigma_8(z=0.61)=0.50\pm 0.12$ and$\sigma_8(z=0.8)=0.39^{+0.11}_{-0.13}$. These values are in excellent agreementwith the extrapolation of a Planck cosmology.

A joint 2- and 3-point clustering analysis of the VIPERS PDR2 catalogue at z~1: breaking the degeneracy of cosmological parameters