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), 728–767. (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 für 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 Kôkyûroku "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 Kôkyûroku "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 Kôkyûroku "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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