91 research outputs found
Universality of the Route to Chaos -- Exact Analysis
The universality of the route to chaos is analytically proven for countably
infinite number of maps by proposing the Super Generalized Boole (SGB)
transformations. As one of the route to chaos, intermittency route was studied
by Pomeau and Manneville numerically. They conjectured the universality in Type
1 intermittency, that the critical exponent of the Lyapunov exponent is
in Type 1 intermittency. In order to prove their conjecture, we showed that for
certain parameter ranges, the SGB transformations are exact and preserve the
Cauchy distribution. Using the property of exactness, we proved that the
critical exponent is for countably infinite number of maps where Type 1
intermittency occurs
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