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Let  = ( T t  )  t   ≥0  be a  C  0 -semigroup on a separable infinite dimensional Banach space X, with generator  A . In this paper, we study the relationship between the single valued extension property of generator A, and the M-hypercyclicity of the  C  0 -semigroup. Specifically, we prove that if A does not have the single valued extension property at λ ∈  i ℝ, then there exists a closed subspace  M  of  X , such that the  C  0 -semigroup  is M-hypercyclic. As a corollary, we get certain conditions of the generator A, for the  C  0 -semigroup to be M-hypercyclic.

M-hypercyclicity of C 0 -semigroup and Svep of its generator