Jacob's ladders, Riemann's oscillators, quotient of two oscillating multiforms and set of metamorphoses of this system

Abstract: In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\sigma=\frac 12$ into a butterfly (=infinite series of M\" obius functions in the region of absolute convergence $\sigma>1$).