  We investigate the formation of resonances in the P33 partial wave with the
emphasis on possible emergence of dynamically generated quasi-bound states as a
consequence of a strong $p$-wave pion attractive interaction in this partial
wave, as well as their possible interaction with the genuine quark excited
states. By using the Laurent-Pietarinen expansion we follow the evolution of
the $S$-matrix poles in the complex energy plane as a function of the
interaction strength. Already without introducing a genuine quark resonant
state, two physically interesting resonances emerge with pole masses around
1200 MeV and 1400 MeV, with the dominant $\pi N$ and $\pi\Delta$ component,
respectively. The added genuine resonant state in the $(1s)^3$ quark
configuration mixes with the lower dynamically generated resonance forming the
physical $\Delta(1232)$ resonance, and pushes the second dynamical resonance to
around 1500 MeV, which allows it to be identified with the $\Delta(1600)$
resonance. Adding a second resonant state with one quark promoted to the $2s$
orbit generates another pole whose evolution remains well separated from the
lower two poles. We calculate the helicity amplitudes at the pole and suggest
that their $Q^2$ dependence could be a decisive test to discriminate between
different models of the $\Delta(1600)$ resonance.
