Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let f and g be C r unimodal maps, with r#8201;#8805;#8201;3, topologically conjugated by h and without periodic attractors. If h is differentiable at a point p in the expanding set E(f), with h#8242;(p)#8800;0, then, there is an open renormalization interval J such that h is a C r diffeomorphism in the basin B(J) of J, and h is not differentiable at any point in I#8201;#8726;#8201;B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnorapos;s interval cycle attractor A then E(f) has full Lebesgue measure.
['Jose F. Alves', 'Vilton Pinheiro', 'Alberto A. Pinto']
I am writing a research paper on a idea Explosion of smoothness for conjugacies between multimodal maps
[{"from": "human", "value": "I am writing a research paper on a idea Explosion of smoothness for conjugacies between multimodal maps"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let f and g be C r unimodal maps, with r#8201;#8805;#8201;3, topologically conjugated by h and without periodic attractors. If h is differentiable at a point p in the expanding set E(f), with h#8242;(p)#8800;0, then, there is an open renormalization interval J such that h is a C r diffeomorphism in the basin B(J) of J, and h is not differentiable at any point in I#8201;#8726;#8201;B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnorapos;s interval cycle attractor A then E(f) has full Lebesgue measure."}]