Dynamic of Time Varying Weighted Backward Shift Operator

we study the hypercyclic and chaotic properties of the time varying weighted backward shift operator $(Tx)(t)=w(t)x(t+a)$ in $L_p(0,\mathrm{\infty })(1\le p<\mathrm{\infty })$ and $C_0[0,\mathrm{\infty })$. And we also analyse the spectral structure of the operators if the spaces are complex.