18 citations · 24 across the 6 of their papers we have counts for
6 papers
Universal Critical Behavior of Transition to Chaos: Intermittency Route
Ken-ichi Okubo, Ken Umeno
The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular,…
Infinite Ergodicity that Preserves the Lebesgue Measure
Ken-ichi Okubo, Ken Umeno
We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (in…
Universality of the Route to Chaos -- Exact Analysis
Ken-ichi Okubo, Ken Umeno
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 ro…
Canonical superdiffusion and energy fluctuation divergence
Ken-ichi Okubo, Ken Umeno
We propose a noble physical model obtained from a Hamiltonian with periodic potential. This model is canonical, reversible and brings about chaotic superdiffusion with energy fluct…
Exact Lyapunov exponents of the generalized Boole transformations
Ken Umeno, Ken-ichi Okubo
The generalized Boole transformations have rich behavior ranging from the \textit{mixing} phase with the Cauchy invariant measure to the \textit{dissipative} phase through the \tex…
New chaos indicators for systems with extremely small Lyapunov exponents
Ken-ichi Okubo, Ken Umeno
We propose new chaos indicators for systems with extremely small positive Lyapunov exponents. These chaos indicators can firstly detect a sharp transition between the Arnold diffus…