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This article is concerned with the isospectral problem \[ -f'' + \frac{1}{4}f = z\omega f + z^2 \upsilon f \] for the periodic conservative Camassa-Holmflow, where $\omega$ is a periodic real distribution in$H^{-1}_{\mathrm{loc}}(\mathbb{R})$ and $\upsilon$ is a periodic non-negativeBorel measure on $\mathbb{R}$. We develop basic Floquet theory for thisproblem, derive trace formulas for the associated spectra and establishcontinuous dependence of these spectra on the coefficients with respect to aweak$^\ast$ topology.

Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow