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- The University of TokyoJP47 papers
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14 papers · 1 filter
Aperiodic chain recurrence classes of -generic diffeomorphisms
Christian Bonatti, Katsutoshi Shinohara
We consider the space of -diffeomorphims equipped with the -topology on a three dimensional closed manifold. It is known that there are open sets in which -generic d…
A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
Christian Bonatti, Katsutoshi Shinohara
We give a -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain r…
Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics
Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estima…
The twisted baker map
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set…
Dynamical system analysis of a data-driven model constructed by reservoir computing
Miki U Kobayashi, Kengo Nakai, Yoshitaka Saiki +1
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures…
Super exponential divergence of periodic points for C^1-generic partially hyperbolic homoclinic classes
Xiaolong Li, Katsutoshi Shinohara
A diffeomorphism f is called super exponential divergent if for every r>1, the lower limit of #Per_n(f)/r^n diverges to infinity as n tends to infinity, where Per_n(f) is the set o…