ビリヤード
ケプラー問題
ベクトル解析
常微分方程式
複素関数論
力学系
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)
n体問題の特異点論
変分問題
非衝突特異性
現在ゼミで読んでいる文献
過去にゼミで読んだ文献(覚えてる範囲で)
S. Tabachnikov, Geometry and billiards. Student Mathematical Library, 30.
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