Related papers: Puzzles of Quasi-Finite Type, Zeta Functions and S…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
In recent years, a variety of variants of multiple zeta values (MZVs) have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include…
In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in $\mathbb{Z}^d$. The minimal shifts are those shifts in which all configurations contain exactly the…
We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…
We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at…
From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to…
[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix elements as well. The derivation of the…
We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…
The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…
In this paper, we define and study four families of Berndt-type integrals, called mixed Berndt-type integrals, which contain (hyperbolic) sine and cosine functions in the integrand function. Using contour integration, these integrals are…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
We study restricted permutations of sets which have a geometrical structure. The study of restricted permutations is motivated by their application in coding for flash memories, and their relevance in different applications of networking…
I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations.
We study zeta functions enumerating submodules invariant under a given endomorphism of a finitely generated module over the ring of ($S$-)integers of a number field. In particular, we compute explicit formulae involving Dedekind zeta…
Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwisely weakly weighted (generalised) quasi-metrics. We then systematise and extend…
In the field of dynamical systems, it is not rare to meet irregular functions, which are typically H{\"o}lder but not Lipschitz (e.g. the Weierstrass functions). Our goal is to scratch the surface of the following question: what happens if…
In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(\Sigma_{m_-,m_+}, \sigma_\phi)$ which generalizes the standard bilateral Bernoulli shifts. The space $\Sigma_{m_-,m_+}$…
In this note, we consider meromorphic univalent functions $f(z)$ in the unit disc with a simple pole at $z=p\in(0,1)$ which have a $k$-quasiconformal extension to the extended complex plane $\hat{\mathbb C},$ where $0\leq k < 1$. We denote…