Bifurcations in the Family of Billiards Associated with the Curvature Flow

Key Points

• This work investigates the dynamical behavior of one-parameter families of billiards under curvature flow, specifically focusing on bifurcations and orbit structures.
• Analyzed one-parameter families of billiards on convex curves (ovals) influenced by curvature flow.
• Examined bifurcations of periodic orbits, specifically period two and normal periodic orbits.
• Proved the destruction of non-convex caustics in the ellipse during deformation through curvature flow.
• Identified bifurcations in the period two orbits and non-Birkhoff orbits of billiards.
• Demonstrated that non-convex caustics of the ellipse are destroyed by curvature flow.
• Provided insights into the dynamical properties of billiards associated with curvature flow.