2002 年度実績報告書

撞球系をモデルとした力学系・カオス・フラクタルの大域解析的研究

研究課題

研究課題/領域番号	13440056
研究機関	広島大学
研究代表者	久保泉広島大学, 大学院・理学研究科, 教授 (70022621)
研究分担者	宍倉光広京都大学, 大学院・理学研究科, 教授 (70192606) 那須正和広島大学, 大学院・工学研究科, 教授 (20006258) 盛田健彦広島大学, 大学院・理学研究科, 教授 (00192782) 田崎秀一早稲田大学, 理工学部, 助教授 (10260150) 印南信宏新潟大学, 理学部, 教授 (20160145)
キーワード	撞球問題 / 離散力学系 / カオス / フラクタル / 記号力学系 / エントロピー / エルゴード理論
研究概要	双曲的開撞球においてSinai-Bowen-Ruelle測度の役割を果たす不変測度をSRB測度の理論の拡張によって統一的に扱えるようにするために,擬SBR測度の定式化を試みた。また、Lasota-Yorke写像の区分的C^2摂動のエルゴード性の研究を行った。複数の無限に広がった熱浴と結合する有限系で、L_1漸近可換性などを有する、C^*力学系について以下の結果を得た:(a)相対エントロピー生成についてのGallavotti-Cohenの揺らぎ定理、(b)非平衡定常状態の局所摂動についての安定性、(c)MacLennan・Zubarev非平衡アンサンブルとの等価性。さらに、間欠的カオス写像のFrobenius-Perron演算子の固有値問題の研究を行った。実力学系と複素力学系との接点に関わる問題として、実単峰写像族の単調性の問題などについては、これまでの辻井正人氏(北海道大)との研究で、放物型不動点をもつ場合の無限の振動の問題について、正則2次微分へのRuelle作用素やFatou座標への誘導写像について調べられ、その困難がより明らかになってきた。高次元力学系についても研究を始め、射影空間の正則写像について、その完全不変多様体は超平面の和に限ることを証明した。また、楕円関数から定義されるLattesの写像の高次元への拡張も構成した。カルタン部分環上の融合積の自己同形に関する研究を行った。また、融合積に関係した新しいフォンノイマン環の構成法を離散群研究のアナロジーの文脈で与え詳しく調べた。共にエルゴード理論、とりわけ軌道同値の話題に関係する研究である。片側フルシフトの拡大的自己同型が定義する力学系(拡大的可逆片側セルオートマトンの力学系)に関して与えられたBoyle-Maassの3つの予想の内の未解決の2つの内の1つを証明した。

研究成果
(23件)

すべてその他

すべて文献書誌 (23件)

[文献書誌] Nobuhiro Asai: "Multiplicative renormalization and generating functions I"Taiwanese Journal of Mathematics. (2003)
[文献書誌] Nobuhiro Asai: "Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures"Proc. Amer. Math. Soc.. (2003)
[文献書誌] Nobuhiro Asai: "Gaussian and Poisson white noises with related characterization theorems"Contemporary Mathematics. 317. (2003)
[文献書誌] H.Honda: "Two-phase coexisting state of n-hexatriacontane in the first-order phase transition"Thermochimica Acta. (2003)
[文献書誌] Tomoki Inoue: "Ergodic sums of non-integrable functions under one-dimensional dynamical systems with indifferent fixed points"Ergodic Theory and Dynamical Systems. (2003)
[文献書誌] Takehiko Morita: "Piecewise $C^2$ perturbation of Lasota-Yorke maps and their ergodic properties"Osaka J. Math. 40. 207-233 (2003)
[文献書誌] Shuichi Tasaki: "On entropy production of a one-dimensional lattice conductor"Quantum Information. V. (2003)
[文献書誌] Shuichi Tasaki: "Fluctuation Theorem, Nonequilibrium Steady States and MacLennan-Zubarev Ensembles of a Class of Large Quantum Systems"Fundamental Aspects of Quantum Physics. (2003)
[文献書誌] Yoshimichi Ueda: "Free product actions and their applications"Quantum Probability and White Noise Analysis. 16. (2003)
[文献書誌] Yoshimichi Ueda: "Fullness, Connes' $＼chi$-groups, and ultra-products of amalgamated free products over Cartan subalgebras"Trans Amer. Math. Soc.. 355. 349-371 (2003)
[文献書誌] Yoshimichi Ueda: "Automorphisms of free product-type and their crossed-products"J. Operator Theory. (2003)
[文献書誌] H.Honda: "Relaxation phenomenon measured as dynamical specific heat in first-order phase transition of molecular crystal"Physical Review. B65(10). 104112 (2002)
[文献書誌] Satoshi Ikeda: "Fair Circulation of a Token"IEEE Transactions on Parallel and Distributed Systems. 4. 367-372 (2002)
[文献書誌] Nobuhiro Innami: "Geometry of geodesics for convex billiards and circular billiards"Nihonkai Math. J.. 13. 207-215 (2002)
[文献書誌] Shuichi Tasaki: "Thermodynamic Behaviors of Large Dynamical Systems -quantum ld conductor and classical multibaker map -"Lecture Notes in Physics. 597. 395-412 (2002)
[文献書誌] Shuichi Tasaki: "Irreversibility in reversible multibaker maps"Advances in Chemical Physic. 122. 70-107 (2002)
[文献書誌] Shuichi Tasaki: "Spectral Properties of a Piecewise Linear Intermittent Map"Journal of Statistical Physics. 109. 803-820 (2002)
[文献書誌] Yoshimichi Ueda: "Irreducible subfactors of $L({\＼mathbb F}_{＼infty})$ of index $＼laimbda > 4$"J. reine angew. Math.. 548. 149-166 (2002)
[文献書誌] Michiko Yuri: "Weak Gibbs measures and the local producrt structure"Ergodic Theory and Dynamical Systems. 22. 1933-1945 (2002)
[文献書誌] Michiko Yuri: "Multifractal Analysis of weak Gibbs measures for Intermittent systems"Communications in Mathematical Physics. 230. 365-388 (2002)
[文献書誌] Michiko Yuri: "On the speed of convergence to equilibrium states for multi-dimensional maps with indifferent periodic points"Nonlinearity. 15. 429-455 (2002)
[文献書誌] Masakazu Nasu: "The dynamics of expansive invertible onesided cellular automata"Trans. Amer. Math. Soc.. 354. 4067-4084 (2002)
[文献書誌] Masakazu Nasu: "The dynamics of expansive invertible onesided cellular automata"Trans. Amer. Math. Soc.. 354. 4067-4084 (2002)

2002 年度 実績報告書

撞球系をモデルとした力学系・カオス・フラクタルの大域解析的研究

研究代表者

久保 泉 広島大学, 大学院・理学研究科, 教授 (70022621)

研究成果

[文献書誌] Nobuhiro Asai: "Multiplicative renormalization and generating functions I"Taiwanese Journal of Mathematics. (2003)

[文献書誌] Nobuhiro Asai: "Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures"Proc. Amer. Math. Soc.. (2003)

[文献書誌] Nobuhiro Asai: "Gaussian and Poisson white noises with related characterization theorems"Contemporary Mathematics. 317. (2003)

[文献書誌] H.Honda: "Two-phase coexisting state of n-hexatriacontane in the first-order phase transition"Thermochimica Acta. (2003)

[文献書誌] Tomoki Inoue: "Ergodic sums of non-integrable functions under one-dimensional dynamical systems with indifferent fixed points"Ergodic Theory and Dynamical Systems. (2003)

[文献書誌] Takehiko Morita: "Piecewise $C^2$ perturbation of Lasota-Yorke maps and their ergodic properties"Osaka J. Math. 40. 207-233 (2003)

[文献書誌] Shuichi Tasaki: "On entropy production of a one-dimensional lattice conductor"Quantum Information. V. (2003)

[文献書誌] Shuichi Tasaki: "Fluctuation Theorem, Nonequilibrium Steady States and MacLennan-Zubarev Ensembles of a Class of Large Quantum Systems"Fundamental Aspects of Quantum Physics. (2003)

[文献書誌] Yoshimichi Ueda: "Free product actions and their applications"Quantum Probability and White Noise Analysis. 16. (2003)

[文献書誌] Yoshimichi Ueda: "Fullness, Connes' $＼chi$-groups, and ultra-products of amalgamated free products over Cartan subalgebras"Trans Amer. Math. Soc.. 355. 349-371 (2003)

[文献書誌] Yoshimichi Ueda: "Automorphisms of free product-type and their crossed-products"J. Operator Theory. (2003)

[文献書誌] H.Honda: "Relaxation phenomenon measured as dynamical specific heat in first-order phase transition of molecular crystal"Physical Review. B65(10). 104112 (2002)

[文献書誌] Satoshi Ikeda: "Fair Circulation of a Token"IEEE Transactions on Parallel and Distributed Systems. 4. 367-372 (2002)

[文献書誌] Nobuhiro Innami: "Geometry of geodesics for convex billiards and circular billiards"Nihonkai Math. J.. 13. 207-215 (2002)

[文献書誌] Shuichi Tasaki: "Thermodynamic Behaviors of Large Dynamical Systems -quantum ld conductor and classical multibaker map -"Lecture Notes in Physics. 597. 395-412 (2002)

[文献書誌] Shuichi Tasaki: "Irreversibility in reversible multibaker maps"Advances in Chemical Physic. 122. 70-107 (2002)

[文献書誌] Shuichi Tasaki: "Spectral Properties of a Piecewise Linear Intermittent Map"Journal of Statistical Physics. 109. 803-820 (2002)

[文献書誌] Yoshimichi Ueda: "Irreducible subfactors of $L({\＼mathbb F}_{＼infty})$ of index $＼laimbda > 4$"J. reine angew. Math.. 548. 149-166 (2002)

[文献書誌] Michiko Yuri: "Weak Gibbs measures and the local producrt structure"Ergodic Theory and Dynamical Systems. 22. 1933-1945 (2002)

[文献書誌] Michiko Yuri: "Multifractal Analysis of weak Gibbs measures for Intermittent systems"Communications in Mathematical Physics. 230. 365-388 (2002)

[文献書誌] Michiko Yuri: "On the speed of convergence to equilibrium states for multi-dimensional maps with indifferent periodic points"Nonlinearity. 15. 429-455 (2002)

[文献書誌] Masakazu Nasu: "The dynamics of expansive invertible onesided cellular automata"Trans. Amer. Math. Soc.. 354. 4067-4084 (2002)

[文献書誌] Masakazu Nasu: "The dynamics of expansive invertible onesided cellular automata"Trans. Amer. Math. Soc.. 354. 4067-4084 (2002)

2002 年度実績報告書

久保泉広島大学, 大学院・理学研究科, 教授 (70022621)