Symmetry and horseshoe in the model of bouncing ball |
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Authors: | Jianhua Xie |
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Institution: | (1) Department of Applied Mechanics and Engineering, Southwest Jiaotong University, 610031 Chengdu, China |
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Abstract: | 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. |
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Keywords: | bouncing ball symmetry horseshoe symbolic dynamics |
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