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In this paper, we characterize the boundedness, the compactness and theHilbert-Schmidt property for composition operators acting from a deBranges-Rovnyak space $\mathcal H(b)$ into itself, when $b$ is a rationalfunction in the closed unit ball of $H^\infty$ (but not a finite Blaschkeproduct). In particular, we extend some of the results obtained by D. Sarasonand J.N. Silva in the context of local Dirichlet spaces.

Composition Operators On De Branges-rovnyak Spaces Associated To A Rational (Not Inner) Function