The functional limit theorem for the canonical $U$-processes defined on dependent trials

The functional limit theorem is proven for a sequence of normalized $U$-statistics (the socalled $U$-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of $\varphi$-mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.