  This paper examines the coefficient problems for the class of semigroup
generators, a topic in complex dynamics that has recently been studied in
context of geometric function theory. Further, sharp bounds of coefficient
functional such as second order Hankel determinant, third order Toeplitz and
Hermitian-Toeplitz determinants are derived. Additionally, the sharp growth
estimates and the bounds of difference of successive coefficients are
determined, which are used to prove the Bohr and the Bohr-Rogosinski phenomenon
for the class of semigroup generators.
