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**Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in uniformly rotating polytropic stellar models and show that the phase space structure has a mixed character, regions of chaotic rays coexisting with stable structures. Correspondingly, the high-frequency acoustic spectrum is a superposition of frequency subsets associated with dynamically independent phase space regions. The sub-spectra associated with chaotic regions are irregular but with generic statistical properties. In contrast, for the subset of regular modes, which are the easiest to observe and identify, one can construct a precise asymptotic theory. Comparisons with 2D numerical simulations of oscillations in polytropic stellar models show that both the frequency and amplitude distributions of these modes can accurately be described by our asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.**

**References:**

F. Lignières & B. Georgeot, Phys. Rev. E 78, 016215 (2008).

F. Lignières & B. Georgeot, A&A 500, 1173-1192 (2009).

M. Pasek, B. Georgeot, F. Lignières & D. R. Reese, Phys. Rev. Lett. 107, 121101 (2011).

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