Papers in Journals

A trial symbolic dynamics of the planar three-body problem,
in the Proceedings of the Workshop held in St. Petersberg, August 25 - 30, 2007,
Tanikawa, K. and Mikkola, S.: eprint arXiv:0802.2465, 02/2008

The rectilinear three-body problem using symbol sequences II. Role of periodic orbits,
in Few-Body Problem: Theory and Computer Simulations,
Saito, M.M. and Tanikawa, K., Annales Universitatis Turkuensis, Turku, 33 - 38 (2006), eprint arXiv:0711.1957, 11/2007

On Mather's connecting orbits in the standard mapping,
Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys. Vol.119, No.4, (2008, in press).

The rectilinear three-body problem,
Orlov, V.V., Petrova, A.V., Tanikawa, K., Saito, M.M., and Martynova, A.I., Celestial Mechanics and Dynamical Astronomy, Vol.100, 93 - 120, 2008.

A new set of variables in the three-body problem,
Kenji Hiro Kuwabara and Kiyotaka Tanikawa, Celestial Mechanics and Dynamical Astronomy, 2007 (submitted).
eprint arXiv:nlin/0703052

Non-Birkhoff periodic orbits of Farey type and dynamical ordering in the standard mapping II,
Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys. Vol.118, No.4, 675 - 699 (2007).

Subsystems in a stable planetary system: A classification,
K. Tanikawa and T. Ito, Publ.Asron.Soc.Japan Vol.59, No.5, 989 - 1004 (2007).

Numerical experiments of the planar equal-mass three-body problem: The effects of rotation,
Kenji Hiro Kuwabara and Kiyotaka Tanikawa, Chaos Vol.17, 033105 (2007).

Correlation of macroscopic instability and Lyapunov times in the general three-body problem,
Seppo Mikkola and Kiyotaka Tanikawa, Mon.Not.Roy.Astron.Soc. Lett. Vol.379, Issue 1, L21 - L24 (2007).

The rectilinar three-body problem using symbol sequence I. Role of triple collision,
M.M. Saito and K. Tanikawa, Celestial Mechanics & Dynamical Astronomy Vol.98, 95 - 120 (2007).

Trends in 20th Century Celestial Mechnics,
T. Ito and K. Tanikawa, PNAOJ, Vol. 9, 55 - 112 (2007).

Non-Birkhoff periodic orbits of Farey type and dynamical ordering in the standard mapping,
Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys. Vol.117, No.4, 601 - 632 (2007).

  • Order of appearance of homoclinic points in the Henon Map,
    Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys. Vol.116, No.6, 1029 - 1049 (2006).

  • Increase of Topological Entropy until the Three-Fold Horseshoe is Completed
    Y. Yamaguchi and K. Tanikawa Progr. Theor. Phys. Vol.116, No.5, 803 - 817 (2006).

  • An extension of the theorems of three-tangents and three-normals,
    K. Kuwabara and K. Tanikawa, Physics Letters A, Vol.354, Issues 5-6, 445 - 448 (2006).

  • Symmetric periodic orbits and topological entropy in the two-dimensional cubic map,
    Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys., Vol.114, No.6, 1163 - 1177 (2005).

  • Generalized Dynamical Ordering and Topological Entropy in the Henon Map,
    Y. Yamaguchi and K. Tanikawa, Progr. Theor. Phys., Vol.114, No.4, 763 - 791 (2005).

  • Dynamical Ordering of Symmetric Periodic Orbits in the Area Preserving Henon Map,
    Y. Yamaguchi and K. Tanikawa: Progr. Theor. Phys., Vol.113, 935 - 951 (2005).

  • Reversing Symmetries in a Two-Parameter Family of Area-Preserving Maps
    K. Zare and K. Tanikawa: Prog. Theor. Phys. Vol.113, 251 - 259 (2005).

  • Generalized horseshoes in the standard mapping,
    K. Tanikawa and Y. Yamaguchi: Progr. Theor. Phys. Vol.113, 261 - 281 (2005).

  • Units of Time in Ancient China and Japan,
    M. Soma, K. Kawabata, and K. Tanikawa, Publ. Astron. Soc. Japan Vol.56, 887 - 904 (2004).

  • ΔT and the Tidal Acceleration of the Lunar Motion from Eclipses Observed at Plural Sites
    Kiyotaka Tanikawa and Mitsuru Soma, Publ. Astron. Soc. Japan vol.56, 879 - 885 (2004).

  • A solar eclipse versified in Shih Ching
    Kin-aki Kawabata, Kiyotaka Tanikawa, and Mitsuru Soma, Publ. Astron. Soc. Japan Vol.56, 869 - 877 (2004).

  • Periodic orbits in the quadruply reversible non-twist Harper map,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.111, No.5, 757 - 762 (2004).

  • Oscillatory orbits in the standard mapping,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.111, No.5, 689 - 705 (2004).

  • On the symmetric collinear four-body problem,
    M. Sekiguchi and K. Tanikawa, Publ. Astron. Soc. Japan Vo.56, No.1, 235 - 251(2004).

  • On the totality of the eclipse in AD628 in the Nihongi,
    K. Tanikawa and M. Soma, Publ. Astron. Soc. Japan Vol.56, No.1, 215 - 224(2004).

  • Topological entropy in a forced Duffing system
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.110, No.5, 861 - 874(2003).

  • Non-Birkhoff orbits with 2n turning-points in the Standard Map ・ (ps ファイル) ・pdf ファイル
    K. Tanikawa and Y. Yamaguchi, Prog. Theor. Phys. Vol.109, No.2, 187-202(2003).

  • Non-symmetric periodic points in reversible maps: examples from the standard map
    K. Tanikawa and Y. Yamaguchi, Prog. Theor. Phys. Vol.108, No.6, 987-997(2002).

  • Dynamical ordering of periodic accelerator modes in the standard mapping,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vo.108, No.4, 669-678(2002).

  • Long-term integrations and stability of planetary orbits in our solar system,
    T. Ito and K. Tanikawa, Mon. Not. R. Astron. Soc. vol.336, 483-500(2002).

  • Reversible maps in two degrees of freedom Hamitonian systems,
    K. Zare and K. Tanikawa, Chaos, Vol.12, No.3, 699-705(2002).

  • Non-Birkhoff periodic orbits in a circle mapping,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.108, No.2, 231-240(2002).

  • Dynamical ordering of non-Birkhoff orbits and topological entropy in the Standard Mapping,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.107, No.6, 1117-1145(2002).

  • 日本書紀天文記録の信頼性
    Reliability of astronomical records in the Nihongi
    Kin-aki KAWABATA, Kiyotaka TANIKAWA, and Mitsuru SOMA, 国立天文台報 Vol.5, 145-159(2002).

  • Dynamical ordering of symmetric non-Birkhoff periodic points in reversible monotone twist mappings,
    K. Tanikawa and Y. Yamaguchi, Chaos Vol.12, Issue 1, 33-41(2002).

  • Dynamical ordering of non-Birkhoff periodic orbits in forced pendulums,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.106 No.6, 1097-1114(2001).

  • Non-symmetric non-Birkhoff period-2 orbits in the standard mapping,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.106, 691-696(2001).

  • Improvement of triple-encounter criterion,
    H. Umehara and K. Tanikawa, Publ. Astron. Soc. Japan Vol.53, 693-697(2001).

  • Running homoclinic and periodic points in standard-like mappings,
    K. Tanikawa and Y. Yamaguchi, Prog. Theor. Phys. Vol.105, 399-407(2001).

  • Geometrical approach to the splitting of separatrix for standard-like mappings,
    Y. Yamaguchi and K. Tanikawa, Physics letters A280, 33-36(2001).

  • Stability of terretrial protoplanet system and alignment of orbital elements
    Takashi Ito and Kiyotaka Tanikawa, Publ. Astron. Soc. Japan Vol.53, 143-151(2001).

  • Symmetrical non-Birkhoff period-3 orbits in the standard-like mappings,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. Vol.104, 943-954(2000).

  • Binary and triple collisions causing instability in the free-fall three-body problem,
    H. Umehara and K. Tanikawa, Celestial Mechanics & Dynamical Astronomy Vol.76, 187-214(2000).

  • A Search for collision orbits in the free-fall three-body problem II.
    Kiyotaka Tanikawa, Celestial Mechanics & Dynamical Astronomy Vol.76, 157-185(2000).

  • One-dimensional three-body problem via symbolic dynamics,
    K. Tanikawa and S. Mikkola, Chaos Vol.10, 649-657(2000).

  • Homoclinic intersection in C^2 standard-like mappings, ,
    Y. Yamaguchi and K. Tanikawa, Prog. Theor. Phys. 103, 1127-1136(2000).

  • Triple collision in the one-dimensional three-body problem, ,
    K. Tanikawa and S. Mikkola, Celestial Mechanics & Dynamical Astronomy, Vol.76, 23-34(2000).

  • Algorithmic regularization of the few-body problem,,
    S. Mikkola and K. Tanikawa, Monthly Notices of Royal Astronomical Society 310, 745-749(1999).

  • Explicit symplectic algorithm for time-transformed Hamiltonians, ,
    S. Mikkola and K. Tanikawa, Celestial Mechanics & Dynamical Astronomy 74, 287-295(1999).

  • Orbital distribution arbitrarily close to the homothetic equilateral triple collision in the free-fall three-body problem with equal masses ,
    Hiroaki Umehara and Kiyotaka Tanikawa, Celestial Mechanics & Dynamica Astronomy 74, 69-94(1999).

  • A Remark on the Smoothness of Critical KAM Curves in the Standard Mapping,
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa, Prog. Theor. Phys., Vol.101 No.1, 1-24(1999).

  • Stability and instability of the terrestrial protoplanet system and their possible roles in the final stage of planete formation ,
    Takashi Ito and Kiyotaka Tanikawa, Icarus Vol.139, 336-349(1999).

  • Oscillatory orbits in the planar three-body problem with equal masses ,
    Kiyotaka Tanikawa and Hiroaki Umehara, Celestial Mechanics & Dynamical Astronomy Vol.70, 167-180, 1998.

  • On the Appearance Order of Homoclinic and Heteroclinic Intersections in a Family of Dissipative Maps of the Plane ,
    Kiyotaka Tanikawa and Yoshihiro Yamaguchi, Chaos, Solitons, & Fractals 9, 1497-1512(1998).

  • Does Kozai resonance drive CH Cygni? ,
    Seppo Mikkola and Kiyotaka Tanikawa, Astronomical Journal, 116(1998), 444-450.

  • A search for collision orbits in the free-fall three-body problem I. Numerical procedure ,
    K. Tanikawa, H. Umehara, and H. Abe
    Celestial mechanics & Dynamical Astronomy 62(1995), 335-362.

  • Binaries in the universe. Possible dynamical mechanisms of formation, evolution and disruption of different kinds of constituents of the universe ,
    J. Anosova and K. Tanikawa, Astrophysics & Space Science 234(1995), 191-205.

    Papers in Proceedings

  • Multiple collisions in the one-dimensional Free-Fall Four-Body Problem,
    K. Tanikawa and S. Mikkola
    in the Proc. 32nd Symposium on Celestial mechanics, Hayama, Kanagawa, pp.297-310, 2000.

  • Lifespan of organisms and the secular change of the environment
    K. Tanikawa, T. Handa, and T. Ito
    in the Proc. 32nd Symposium on Celestial Mecjanics, pp.179-193, 2000.

  • Space occultation
    K. Tanikawa and Y. Mikami
    in the Proc. 32nd Symposium on Celestial Mecjanics, pp.228-233, 2000.

  • A condition for the existence of homoclinic intersection in the C^2 standard-like mappings
    Y. Tamaguchi and K. Tanikawa
    in the Proc. 32nd Symposium on Celestial Mecjanics, pp.261-271, 2000.

  • Symmetrical non-Birkhoff period-3 orbits in the standard-like mappings
    Y. Tamaguchi and K. Tanikawa
    in the Proc. 32nd Symposium on Celestial Mecjanics, pp.272-282, 2000.

  • Long-term stability of our solar system
    T. Ito and K. Tanikawa
    in the Proc. 32nd Symposium on Celestial Mecjanics, pp.47-96, 2000.

  • Slingshot-escape condition in the planar three-body problem
    H. Umehara and K. Tanikawa
    In 'The Chaotic Universe'(eds. V.G. Gurzadian and R.Ruffini), World Scientific, pp.568-578, 2000.

  • One dimensional three-body problem via symbolic dynamics
    K. Tanikawa and S. Mikkola
    力学系の特異現象とその数理，数理解析研究所講究録1118，pp.67-83， December, 1999.

  • Effect of Jovian Planets on the Stability of Terrestrial Protoplanet Systems
    T. Ito and K. Tanikawa
    in Star formation 1999.

  • Collision orbits and chaos in the free-fall three-body problem
    Kiyoaka Tanikawa and Hiroaki Umehara
    Structure & Evolution of Stellar Systems, Proceedings of the international Conference, Pertozavodsk, Russia, held on 13-17 August, 1995, pp.65-68 (1997).

  • 自由落下三体問題における衝突軌道、振動運動とカオス
    谷川清隆, 総合研究大学院大学 共同研究「非線形現象の数理科学ワークショップ」 報告、1997

  • Possible formation of flows inside and around binary systems of stars and galaxies
    Joanna Anosova and Kiyotaka Tanikawa
    Structure & Evolution of Stellar Systems, Proceedings of the international Conference, Pertozavodsk, Russia, held on 13-17 August, 1995, pp.62-64 (1997).

  • Dominat role of collisions in the Free-fall three-body problem
    H. Umehara and K. Tanikawa,
    in Chaos in Gravitational N-Body Systems, Kluwer Academic Publishers (eds. Muzzio,J., Ferraz-Mello,S., and Henrard,J.), pp.285-290, 1996.

  • Triple Collision and Escape in the Three-Body Problem
    H. Umehara, K. Tanikawa, and Y. Aizawa,
    in Dynamical Systems and Chaos, Vol.2 (eds. Y.Aizawa, S.Saito, and K.Shiraiwa), World Scientific, 1995, pp. 404-407.

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