12 citations · 54 across the 27 of their papers we have counts for
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Non-existence of Lyapunov exponents in the Newhouse domain
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
We show that within the Newhouse domain of surface diffeomorphisms (), there exists a dense subset such that for any , Lyapu…
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
Dongchen Li, Xiaolong Li, Katsutoshi Shinohara +1
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for ($…
Abundance of observable Lyapunov irregular sets
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
Lyapunov exponent is widely used in natural science to find chaotic signal, but its existence is seldom discussed. In the present paper, we consider the problem of whether the set…
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…