Stickiness in chaotic billiards with n-fold symmetry

Abstract In this work, we study a family of chaotic billiards with the main characteristic of presenting only $$C_n$$ C n rotational symmetries. The billiard repeats itself under rotations of $$2\pi /n$$ 2 π / n , where here, n is called the symmetry parameter. Due to collisions with straight segments, the phase space exhibits stickiness regions that occur within the chaotic sea, without the formation of stability islands, thereby ensuring the ergodicity of the system. We investigate the expansion of these regions in phase space and their dependence on the symmetry parameter n and on the radii of the circumferences that define the billiard boundary. Our results show that independent of the geometric parameters and the rotational symmetry, the trapping-time distributions follow a power law decay with the $$\gamma \simeq 3$$ γ ≃ 3 as other well-known distributions.