Haruyoshi Tanaka's Home Page


 CONTACT 

Haruyoshi Tanaka, Ph.D.

Department of Mathematics and Statistics
Wakayama Medical University
Wakayama City 6418509
Japan

htanaka

Telephone:
Office: 81 73 447 2300 (4839)

 AREAS OF INTEREST 

probability theory, ergodic theory, thermodynamic formalism, symbolic dynamics, perturbation theory, fractal sets, iterated function systems.

 PAPERS 

Quasi-compactness of transfer operators for topological Markov shifts with holes, submitted. (arXiv)

Higher-order asymptotic behaviours of pressure functionals and statistical representations of the coefficients, submitted.

General asymptotic perturbation theory in transfer operators, submitted. (arXiv)

Asymptotic solution of Bowen equation for perturbed potentials on shift spaces with countable states, to appear in J. Fractal Geom. (Old version : arXiv)

Convergence of the Gibbs measures of perturbed graph iterated functions systems with degeneration, Far East J. Dynam. Sys. 32, 105-138, (2020).

Perturbed finite-state Markov systems with holes and Perron complements of Ruelle operators, Israel J. of Math. 236, (2020), 91-131.

Perturbation analysis in thermodynamics using matrix representations of Ruelle operators and its application to graph IFS, Nonlinearity, 32, (2019), 728767. (Old version : arXiv)

Asymptotic perturbation of graph iterated function systems, Journal of Fractal Geometry, 3 (2016), 119--161.

An asymptotic analysis in thermodynamic formalism, Monatshefte f黵 Mathematik, 164 (2011), 467-486.

Spectral properties of a class of generalized Ruelle operators, Hiroshima Mathematical Journal, 39 (2009), 181-205. (pdf)

(with Morita, T.), Singular perturbation of symbolic dynamics via thermodynamic formalism, Ergodic Theory and Dynamical Systems, 28 (2008), 1261-1289.

 OTHERS 

Asymptotic behaviours of pressure functionals and statistical representations of the coefficients, RIMS K鬹y鹯oku "Integrated Research on Random Dynamical Systems and Multi-Valued Dynamical Systems", 2217 (2022), 51-61.

Asymptotic solution of Bowen equation for perturbed potentials defined on shift spaces, RIMS K鬹y鹯oku "Research on the Theory of Random Dynamical Systems and Fractal Geometry", 2176 (2021), 28-36.

Invariant measure of perturbed graph-directed IFS with degeneration, RIMS K鬹y鹯oku "Integrated Research on the Theory of Random Dynamical Systems", 2115 (2019), 73-82.

On singular perturbation of symbolic dynamics with a finite number of transitive components, Bulletin of Liberal Arts and Sciences, Wakayama Medical University, 42 (2012), 1-20. Bulletin Paper

Doctoral's thesis:「ある種の一般化されたRuelle作用素のスペクトル的性質」 ( Spectral properties of a class of generalized Ruelle operators ), 広島大学, (2009).

Lecture (lectures at Wakayama Medical University)



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