ビリヤード

• ELCAS(高校生向け，2017年度)

ケプラー問題

• ILASセミナー(2017年度)

ベクトル解析

• 微分積分学続論I(京大)

常微分方程式

• 微分積分学続論II(京大)，数学A(阪大)

複素関数論

• 工業数学A1(京大)

力学系

• 力学系理論(阪大)

可積分ハミルトン系とその摂動 (KAM理論)

• 数理物理学通論(京大，2016年度，2018年度，2019年度)

• 集中講義(首都大，慶應大)

• 参考文献「ハミルトン力学系」(サイエンス社)

n体問題の特異点論

• 九州大学集中講義(2022年)

Aubry-Mather理論と逆KAM理論

制限3体問題とHill問題の導出

変分問題

• 数理物理学通論(京大，2017年度)

• 特別講義 解析学A「n体問題の周期解の変分解析」(神戸大学集中講義, 2017年度)

非衝突特異性

• 2005年度力学系理論勉強会「ハミルトン系の周期軌道と変分法」

現在ゼミで読んでいる文献

• S. Tabachnikov,  Geometry and billiards. Student Mathematical Library, 30. 

過去にゼミで読んだ文献(覚えてる範囲で)

• J. Moser, Monotone twist mappings and the calculus of variations.Ergodic Theory Dynam. Systems6(1986), no.3, 401–413.

• G. Fei, Multiple periodic solutions of differential delay equations via Hamiltonian systems I

• 木下宙，天体と軌道の力学，東京大学出版会，1998年

• P. H. Rabinowitz, A note on a class of reversible Hamiltonian systems. Adv. Nonlinear Stud. 9 (2009), no. 4, 815–823. 

• P. H. Rabinowitz, Ed Stredulinsky,  On a class of infinite transition solutions for an Allen-Cahn model equation. Discrete Contin. Dyn. Syst. 21 (2008), no. 1, 319–332. 

• Z. Xia, Arnold diffusion and instability in Hamiltonian dynamics, preprint

• A. Sorrentino, Action-minimizing methods in Hamiltonian dynamics. An introduction to Aubry-Mather theory. Mathematical Notes, 50. Princeton University Press

• Joshua Fitzgerald, Shane D Ross, Theory of low-energy transit orbits in the periodically-perturbed restricted three-body problem, January 2021, Conference: AAS/AIAA Space Flight Mechanics Meeting

• V. I. Arnolʹd,  Geometrical methods in the theory of ordinary differential equations. Springer

• P. H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 5, 331–346. 

• J. N. Mather, Modulus of continuity for Peierls's barrier

• 小磯深幸，曲面の変分問題-極小曲面入門-

• P. Felmer, S. Martínez, K. Tanaka,  High-frequency chaotic solutions for a slowly varying dynamical system.  Ergodic Theory Dynam. Systems 26 (2006), no. 2, 379–407.

• A. Fathi & P. Pageault,  Aubry-Mather theory for homeomorphisms. Ergodic Theory Dynam. Systems 35 (2015), no. 4, 1187–1207.

• I. M. Gel'fand & S. V. Fomin, Calculus of variations, Dover Publications

• John N Mather, Existence of quasiperiodic orbits for twist homeomorphisms of the annulus. Topology 21 (1982), no. 4, 457–467

• V. Bangert, Mather sets for twist maps and geodesics on tori. Dynamics reported, Vol. 1, 1–56

• J. Franks & M. Misiurewicz, Topological Methods in Dynamical Systems, Handbook of Dynamical Systems, Vol 1A, 547---598, Springer (2002)

• J. Mather, A criterion for the nonexistence of invariant circles. Inst. Hautes Études Sci. Publ. Math. No. 63 (1986), 153–204.

• P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations. CBMS Regional Conf. Ser. in Math. 65

• R. Bott & L. W. Tu, Differential Forms in Algebraic Topology, Springer

• J. N. Mather,  Dynamics of area preserving maps. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 1190–1194. 

• Eiko Kin, Hiroaki Nakamura, Hiroyuki Ogawa, Lissajous 3-braids, preprint

• P. H. Rabinowitz, The Calculus of Variations and the Forced Pendulum

• P. H. Rabinowitz, Heteroclinics for a Hamiltonian system of double pendulum type. Topol. Methods Nonlinear Anal. 9 (1997), no. 1, 41–76.

• K.-C. Chen & G. Yu, Syzygy sequences of the N-center problem. Ergodic Theory Dynam. Systems 38 (2018), no. 2, 566–582.

• R. Ortega, Instability of periodic solutions obtained by minimization, The first 60 years of nonlinear analysis of Jean Mawhin, 189–197, World Sci. Publ., River Edge, NJ, 2004.

• W. B. Gordon, A minimizing property of Keplerian orbits. Amer. J. Math. 99 (1977), no. 5, 961–971.

• R. L. Devaney, Collision orbits in the anisotropic Kepler problem. Invent. Math. 45 (1978), no. 3, 221–251.

• T. J. Hunt & R. S. MacKay, Anosov parameter values for the triple linkage and a physical system with a uniformly chaotic attractor. Nonlinearity 16 (2003), no. 4, 1499–1510.

• 西川青季, 幾何学的変分問題, 岩波書店

• Hirsch, Smale, Devaney 力学系入門 

近いうちにゼミで読むかもしれない(読みたい)文献

• W. Ziller, Geometry of the Katok examples. Ergodic Theory Dynam. Systems 3 (1983), 135–157.

• L. T. Butler & A. Sorrentino, Alfonso, Weak Liouville-Arnolʹd theorems and their implications. Comm. Math. Phys. 315 (2012), 109–133.

• A. Delshams, R. de la Llave & T. M.  Seara,  A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model. Mem. Amer. Math. Soc. 179 (2006), no. 844

• V. Kaloshin & K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

• G. D. Birkhoff,  Dynamical systems