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LetBX andBY be the open unit balls of the Banach SpacesX and Y , respectively. Let V and W be two countable families of weights on BX and BY , respectively. Let HV (BX) (or HV0 (BX)) and HW (BY ) (or HW0 (BY )) be the weighted Fr echet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings : BX ! BY and : BX ! C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY ) (or HW0 (BY )): Also, we ob- tained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

Weighted composition operators and‎ ‎dynamical systems on weighted Spaces of holomorphic functions on‎ ‎Banach spaces