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

This article is concerned with the isospectral problem $-f'' + \frac{1}{4} f = zωf + z^2 \upsilon f$ for the periodic conservative Camassa-Holm flow, where $ω$ is a periodic real distribution in $H^{-1}_{\mathrm{loc}}(\mathbb{R})$ and $\upsilon$ is a periodic non-negative Borel measure on $\mathbb{R}$. We develop basic Floquet theory for this problem, derive trace formulas for the associated spectra and establish continuous dependence of these spectra on the coefficients with respect to a weak$^\ast$ topology.

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