Shigehiro Ushiki = Some Papers


Julia Sets with Polyhedral Symmetries

Proceedings of the International Conference "Dynamical Systems and Related Topics", 3-7 September 1990, Nagoya, Japan.
Editor K.Shiraiwa, Advanced Series in Dynamical Systems Vol 9. pp515-538. World Scientific Publishing Company, Singapore, 1991.


Julia Sets with Polyhedral Symmetries

Fractals in the Fundamental and Applied Sciences, Proceedings of the First IFIP Conference on Fractals in the Fundamental and Applied Sciences, Lisbon, Prtugal, 6-8 June, 1990. pp425-442.
H.-O. Peitgen, J.M.Henriques & L.F.Penedo (Editors) Elsevier Science Publishers B.V. (North-Holland), IFIP, 1991.


Boettcher's Theorem and Super-Stable Manifolds for Multidimensional Complex Dynamical Systems

Advanced Series in Dynamical Systems, Vol.11, Proceedings of the RIMS Conference Structure and Bifurcations of Dynamical Systems 18-21 February 1991 Kyoto, ed. S.Ushiki. World Scientific, pp168-184, 1992.


Super-Stable Manifolds of Super-Saddle-Type Julia Sets in C^2

Advanced Series in Dynamical Systems, Vol.13, Proceedings of the RIMS Conference Chaotic Dynamical Systems, 7-10 July 1992, ed. S.Ushiki, World Scientific, pp165-180, 1993.


Complex Ruelle Operator and Hyperbolic Complex Dynamical Systems

RIMS Kokyuroku 1072,pp50-61, Invariants of Dynamical Systems and Applications, 1998.


Complex Ruelle Operator in a Parabolic Basin

RIMS Kokyuroku 1087,pp108-119, Research on Complex Dynamical Systems --- where it is and where it is going, 1999.


Fredholm Determinant of Complex Ruelle Operator, Ruelle's dynamical zeta-function, and forward/backward Collet-Eckmann Condition

RIMS Kokyuroku 1153, pp85-102, Comprehensive Research on Complex Dynamical Systems and Related Fields, 2000.


Complex Gibbs Measures for Complex Dynamical Systems and Eigen-hyperfunctions of Complex Ruelle Operator

RIMS Kokyuroku 1179, pp69-82, New Developments in Dynamical Systems, 2000.


Second Julia sets of complex dynamical systems in C^2
-- computer visualization --


Exploration of Complex He'non Dynamics

Research on Complex Dynamics and Related Fields, December 6-10, 2010,
edited by Hiroki Sumi, RIMS Kokyuroku 1762, pp100-111.
September 2011, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan.


Critical points and Julia sets of complex He'non maps


Coexisting attractive cycles in He'non dynamics

Talk at RIMS conference on Dynamical Systems (July 10, 2013)


Siegel ball and Reinhardt domain in complex He'non dynamics

Talk at Karuizawa Winter Workshop on Dynamical Systems (January 10, 2015)


Abundance of Siegel balls in a family of complex He'non maps

Talk at Karuzawa Winter Workshop on Dynamical Systems (January 9, 2016)


Parabolic Bifurcation of area-preserving He'non maps

Talk at RIMS conference on Dynamical Systems (May 18, 2016)


Anti-conjugacy of complex dynamical systems and slices of rotation domains

Talk in RIMS conference on Dynamical Systems (August 24, 2017)


An elementary approach to invariant cubic curves of surface automorphisms

Talk on the occasion of the retirement of Prof. Ueda. (March 18, 2017)


Affluence of Siegel balls in surface automorphisms

Talk at RIMS conference on Dynamical Systems (June 6, 2017)


Reversible complex dynamical systems and exotic rotation domains

Talk at RIMS conference on Complex Dynamical Systems (December 12, 2017)


Julia set of a surface automorphism of positive entropy --- an example of J* =/= J

Talk in RIMS conference on Complex Dynamical Systems (December 8, 2018)


Twist dynamics of rational surface


Real slice of complex Surface automorphism and complex Salem number

Talk at Kyoto Dynamical Systems Seminar (April 19, 2019)


Rotation Attractors and Rotation Domains in Complex Surface Automorphisms

Talk at Keio Univ. (July 16, 2019)


Invariant Curves in Complex Surface Automorphisms

Talk at Kyoto Dynamical Systems Seminar (November 1, 2019)


Inavriant Curves in Complex Surface Automorphisms

Talk at Kyoto Dynamical Systems Seminar (March 23, 2020)


Elemetary construction of Complex Surface Automorphisms

Talk at Kyoto Dynamical Systems Seminar (November 20, 2020)


Strange Attractors in Surface Automorphisms

Talk at RIMS conference on Complex Dynamical Systems (Dec. 10, 2020)


Dynamics in the Juia set of a surface automorphism

Talk at Kyoto Dynamical Systems Seminar (Jul. 11,2021)


Elliptic fibrations and periodic curves in surface automorphisms

Talk at Kyoto Dynamical Systems Seminar (Dec. 3, 2021)


Elliptic fibrations and periodic curves in surface automorphisms

Talk at RIMS conference "Complex Dynamical Systems" (Dec. 16, 2021)


Multiple Dynamics on Elliptic Surface

Talk at Kyoto Dynamical Systems seminar (April 22, 2022)


Mordell-Weil Dynamics on Elliptic surface

Talk at Kyoto Dynamical Systems seminar (November 4, 2022)

  • PDF File(24.5MB)

  • Rational Elliptic Surface without Section

    Talk at RIMS symposium on complex dynamical systems (December 14, 2022)

  • PDF File (51.1MB)
  • PDF File (52.1MB)

  • Exotic Rotaion Domains in Complex He'non Dynamics

    Talk st Fench-Japanese atelier, Kyoto (March 27, 2023)

  • PDF File (9.4MB)

  • Herman Rings for Rational Dynamics in P^2

    Talk at Kyoto Dynamical Systems Seminar Oct. 13, 2023.

    PDF File (6.6MB)


    Super-Exotic Rotation Domains in Complex Sueface Automorphisms

    Talk at Kyoto Dynamical Systems Seminar, Apr. 12, 2024.

    PDF File (2142KB)



    Attracting Herman rings for Henon dynamics

    Short communication at Kyoto Dynamical Systems Seminar, Apr. 12, 2024.

    PDF File(6.3MB)