28 citations · 132 across the 43 of their papers we have counts for
44 papers · 1 filter
Decay of correlations and normal approximation for nonstationary heterochaos baker maps
Juho Leppänen, Hiroki Takahasi
We study statistical properties of nonstationary compositions of a sequence of heterochaos baker maps. For maps whose central direction is mostly expanding, we establish three main…
The recurrence spectrum for dynamical systems beyond specification
Hiroki Takahasi
We introduce {\it (W')-specification} in terms of language decompositions of subshifts, and show that any recurrence set of a subshift with this property has full Hausdorff dimensi…
Hausdorff dimension of specification for the -shifts
Hiroki Takahasi
Specification is an important concept in dynamical systems introduced by Bowen. Schmeling proved that the set of such that the corresponding -shift has specification is of…
Large deviation principles for periodic points of the Dyck shift
Hiroki Takahasi
We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of…
Exponential mixing for heterochaos baker maps and the Dyck system
Hiroki Takahasi
We investigate mixing properties of piecewise affine non-Markovian maps acting on or and preserving the Lebesgue measure, which are natural generalizations of t…
Large deviations of homological growth rates for hyperbolic surfaces
Johannes Jaerisch, Hiroki Takahasi
We perform a large deviations analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. For surfaces uniformized by a wide class of Fuchsian groups of the…
Level-2 large deviation principle for countable Markov shifts without Gibbs states
Hiroki Takahasi
We consider level-2 large deviations for the one-sided countable full shift without assuming the existence of Bowen's Gibbs state. To deal with non-compact closed sets, we provide…
Heterochaos baker maps and the Dyck system: maximal entropy measures and a mechanism for the breakdown of entropy approachability
Hiroki Takahasi, Kenichiro Yamamoto
We introduce two parametrized families of piecewise affine maps on and , as generalizations of the heterochaos baker maps which were introduced and investigated…
Hausdorff dimension of sets with restricted, slowly growing partial quotients in semi-regular continued fractions
Yuto Nakajima, Hiroki Takahasi
We determine the Hausdorff dimension of sets of irrationals in whose partial quotients in semi-regular continued fractions obey certain restrictions and growth conditions.…
Multifractal analysis of homological growth rates for hyperbolic surfaces
Johannes Jaerisch, Hiroki Takahasi
We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level…
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…
Hausdorff dimension of sets with restricted, slowly growing partial quotients
Hiroki Takahasi
I. J. Good (1941) showed that the set of irrational numbers in whose partial quotients tend to infinity is of Hausdorff dimension . A number of related results i…
Distribution of cycles for one-dimensional random dynamical systems
Shintaro Suzuki, Hiroki Takahasi
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branch…
Precise asymptotics on the Birkhoff sums for dynamical systems
Lulu Fang, Hiroki Takahasi, Yiwei Zhang
We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These results are parallel to that on the arithmetic sums of independent and identically dis…
Hausdorff dimension of Cantor intersections and robust heterodimensional cycles for heterochaos horseshoe maps
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension three, we introduce a -open set of diffeomorphisms of having two hors…
Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches
Johannes Jaerisch, Hiroki Takahasi
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the mixed mu…
Statistical properties of periodic points for infinitely renormalizable unimodal maps
Hiroki Takahasi
For an infinitely renormalizable negative Schwarzian unimodal map with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infi…
Large deviation principle for harmonic/geometric/arithmetic mean of digits in backward continued fraction expansion
Hiroki Takahasi
We establish the (level-1) large deviation principles for three kinds of means associated with the backward continued fraction expansion. We show that: for the harmonic and geometr…
Existence of Large deviations rate function for any -unimodal map
Hiroki Takahasi, Masato Tsujii
For an arbitrary negative Schwarzian unimodal map with non-flat critical point, we establish the level-2 Large Deviation Principle (LDP) for empirical distributions. We also give a…
Large deviations for denominators of continued fractions
Hiroki Takahasi
We give an exponential upper bound on the probabilitywith which the denominator of the th convergent in the regular continued fraction expansion stays away from the mean $\frac{…
Uniqueness of minimizer for countable Markov shifts and equidistribution of periodic points
Hiroki Takahasi
For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen's Gi…
Piecewise-linear maps with heterogeneous chaos
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between t…
Large Deviation Principle for arithmetic functions in continued fraction expansion
Hiroki Takahasi
Khinchin proved that the arithmetic mean of continued fraction digits of Lebesgue almost every irrational number in diverges to infinity. Hence, none of the classical limit…
Boundary of the horseshoe locus for the Hénon family
Zin Arai, Yutaka Ishii, Hiroki Takahasi
The purpose of this article is to investigate geometric properties of the parameter locus of the Hénon family where the uniform hyperbolicity of a horseshoe breaks down. As an appl…