We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(local...We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.展开更多
基金partially supported by Russian Science Foundation(Grant No.21-41-00018)VD by the Science Fund of Serbia(Grant Integrability and Extremal Problems in Mechanics,Geometry and Combinatorics,MEGIC,Grant No.7744592)the Simons Foundation(Grant No.854861)。
文摘We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.
