Optimization and the Miranda Approach in Detecting Horseshoe-Type Chaos by Computer

f of the underlying abstract theorem avoids of referring to any results of applied algebraic topology and relies only on the Brouwer fixed point theorem. The second novelty is that the process of gaining the subset relations to be checked is, to a large extent, also automatized. The promising subset relations come from solving a constrained optimization problem via the penalty function approach. results and computational methods are demonstrated by finding embedded copies of the standard horseshoe dynamics in iterates of the classical H´enon mapping.

• Type: Journal
• Year: 2007
• Where: IJBC
• Authors: Balázs Bánhelyi, Tibor Csendes, Barnabas M. Garay
• Keywords: Abstract Theorem, IJBC 2007, Promising Subset Relations, Subset Relations