摘要
By coordinate transformation, the map of bouncing ball has certain symmetry in the new coordinates, This symmetry is used to simplify the conditions which guarantee the existence of the compact, hyperbolic and invariant set and to find the same properties in symbolic dynamics. Based on the analysis, the lower bound of parameter beyond which the map possesses a hyperbolic horseshoe is estimated more precisely.
By coordinate transformation, the map of bouncing ball has certain symmetry in the new coordinates, This symmetry is used to simplify the conditions which guarantee the existence of the compact, hyperbolic and invariant set and to find the same properties in symbolic dynamics. Based on the analysis, the lower bound of parameter beyond which the map possesses a hyperbolic horseshoe is estimated more precisely.
