abstract
- We investigate the classical dynamics of a point particle confined within an elliptic billiard under the influence of a uniform gravitational field oriented at an arbitrary angle. Using numerical simulations, we analyze how the combined effects of energy, gravitational inclination, and billiard eccentricity shape the system¿s behavior. Phase-space maps reveal three distinct dynamical regimes: a low-energy regime dominated by quasi-periodic motion, an intermediate regime characterized by chaotic trajectories, and a high-energy regime approaching integrable dynamics. To quantify chaoticity, we compute Lyapunov exponents as a function of energy and angle, identifying a range of angles where chaos is maximized for a variety of eccentricities. In addition, we introduce a geometric symmetry parameter and establish a correlation between dynamical instability and the asymmetry induced by tilted gravity. Our results provide a comprehensive framework for understanding how geometric and energetic factors modulate chaos in non-integrable billiard systems.