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In this paper, we consider the minimal period estimates for brake orbits ofnonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonianfunction $H\in C^2(\Bbb R^{2n}, \Bbb R)$ is super-quadratic and convex, forevery number $\tau>0$, there exists at least one $\tau$-periodic brake orbit$(\tau,x)$ with minimal period $\tau$ or $\tau/2$ provided $H(Nx)=H(x)$.

Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems