Dynamic stability of compact stars

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After some historical remarks we discuss different criteria of dynamical stability of stars, and properties of the critical states where dynamical stability is lost, leading to collapse with formation of the neutron star or a black hole. At the end some observational and theoretical problems related to quark stars are discussed.
To appear in Proc. NATO Advanced Research Workshop on Superdense QCD Matter and Compact Stars. Yerevan, Armenia September 27- October 4, 2003

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