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We explore the effects of the density dependence of symmetry energy on thedynamical instabilities and crust-core phase transition in the cold and warmneutron stars in the RMF theory with point-coupling interactions using theVlasov approach. The role of the temperature and neutrino trapping has alsobeen considered. The distillation effect, crust-core transition density andpressure, the cluster size and growth rates have been discussed. The presentwork shows that the slope of symmetry energy, temperature, and neutrinotrapping have obvious effects.

Dynamical instabilities for model with point-coupling interactions: Vlasov formalism method