Volume growth in the component of fibered twists

For a Liouville domain W whose boundary admits a periodic Reeb flow, we can consider the connected component [τ] π₀(Symp^c(w)) of fibered twists. In this paper, we investigate an entropy-type invariant, called the slow volume growth, in the component [τ] and give a uniform lower bound of the growth using wrapped Floer homology. We also show that [τ] has infinite order in π₀(Symp^c(w)) if there is an admissible Lagrangian L in W whose wrapped Floer homology is infinite dimensional. We apply our results to fibered twists coming from the Milnor fibers of A_k-type singularities and complements of a symplectic hypersurface in a real symplectic manifold. They admit so-called real Lagrangians, and we can explicitly compute wrapped Floer homology groups using a version of Morse-Bott spectral sequences.