[2] Discrete dynamical systems associated with root systems of indefinite type,
Doctral thesis (2001)
[Abstract] [Abstract in Japanese (PDF file)] [Main body (PDF file) ]

[4] Discrete dynamical systems associated with root systems of indefinite type,
Commun. Math. Phys. 224 (2001) 657--681
[Abstract]

[5] Weyl Group Symmetry of Type $D_5^{(1)}$ in the $q-$Painlev\'e V Equation,
(old title: The extended Weyl group $\widetilde{W}(D_5^{(1)})$ as an extension of KNY's birational representation of $\widetilde{W}(A_1^{(1)}\times A_3^{(1)})$),
Funkcial. Ekvac. 46 (2003) 173--186
[Abstract] [Reviews for RIMS kokyuroku (in Japanese) pdf file]

[6] The space of initial conditions for linearisable mappings,
T. Takenawa, M. Eguchi, B. Grammaticos, Y. Ohta, A. Ramani and J. Satsuma,
Nonlinearity {16} 457--478 (2003)
[Abstract] [Reviews for RIMS kokyuroku (in Japanese) PDF file ]

[7] Discrete dynamical systems associated with the configuration space of 8 points in P^3(C),
Comm. Math. Phys. 246 (2004) 19--42
[Abstract] [PDF file]

[8] Integrability of $n$-dimensional dynamical systems of type $E_7^{(1)}$ and $E_8^{(1)}$,
preprint: arXiv:nlin/0409051

[9] On the identity of two $q$-discrete Painleve equations and their geometrical derivation,
B. Grammaticos, A. Ramani and T. Takenawa,
Adv. Difference Equ. Art. (2006) ID 36397, 11 pp.

[10] Elliptic curves and birational representation of Weyl groups,
M. Eguchi and T. Takenawa,
preprint: arXiv:math/0511726

[11] Tropical representation of Weyl groups associated with certain rational varieties,
T. Tsuda and T. Takenawa,
Adv. Math. 221 (2009), 936--954
preprint: arXiv:math/0607661

[12] A class of integrable and nonintegrable mappings and their dynamics,
T. Tsuda, B. Grammaticos, A. Ramani and T. Takenawa,
Lett. Math. Phys. 82 (2007) 39--49

[13] Tropical spectral curves and integrable cellular automata,
R. Inoue and T. Takenawa,
Int. Math. Res. Not. Art. (2008) ID rnn019, 27 pp
preprint: arXiv:0704.2471
[Reviews for RIMS kokyuroku (in Japanese) with R. Inoue and S. Iwao PDF file]

[14] A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice,
R. Inoue and T. Takenawa,
Comm. Math. Phys. 289 (2009), 995--1021
preprint: arXiv:0806.3318

[15] Real ideal and the duality of semidefinite programming for polynomial optimization,
Y. Sekiguchi, T. Takenawa and H. Waki,
JJIAM, 30 (2013) 321--330
preprint: arXiv:0901.2998

[16] Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic,
R. Inoue and T. Takenawa,
Expansion of integrable systems, RIMS Kokyuroku Bessatsu, B13 (2009) 175--190
preprint: arXiv:0902.0448

[17] A classification of two-dimensional integrable mappings and rational elliptic surfaces,
A. S. Carstea and T. Takenawa,
J. Phys. A, 45 (2012), Article ID:155206, 15 pp
preprint: arXiv:1005.3586

[18] A note on minimization of rational surfaces obtained from birational dynamical systems,
A. S. Carstea and T. Takenawa,
JNMP, 20:sup 1 (2013) 17--33
preprint: arXiv:1211.5393

[19] On the (non-)differentiability of the optimal value function when the optimal solution is unique,
Daisuke Oyama and Tomoyuki Takenawa,
Journal of Mathematical Economics (2018) in press
preprint: SSRN:2373092

[20] Discrete Schlesinger transformations, their Hamiltonian formulation, and difference Painleve equations,
Anton Dzhamay, Hidetaka Sakai and Tomoyuki Takenawa,
preprint: arXiv:1302.2972

[21] Geometric analysis of reductions from Schlesinger transformations to difference Painleve equations,
Anton Dzhamay and Tomoyuki Takenawa,
Algebraic and analytic aspects of integrable systems and Painleve equations, 87--124,
Contemp. Math., 651, Amer. Math. Soc., Providence, RI, 2015
preprint: arXiv:1408.3778

[22] Fiber-dependent deautonomization of integrable 2D mappings and discrete Painleve equations,
Adrian Stefan Carstea, Anton Dzhamay and Tomoyuki Takenawa,
J. Phys. A: Math. Theor. 50 (2017) Article ID:405202, 41 pp (Open Access until September 2018)
preprint: arXiv:1702.04907

[23] On some applications of Sakai's geometric theory of discrete Painlev\'e equations,
Anton Dzhamay and Tomoyuki Takenawa,
SIGMA Symmetry Integrability Geom. Methods, 14 (2018) 075, 20pp

[24] Space of initial conditions and geometry of two 4-dimensional discrete Painlev\'e equations
Adrian Stefan Carstea and Tomoyuki Takenawa,
J. Phys. A, 52 (2019) 275201, 25pp

[25] Super-QRT and 4D-mappings reduced from the lattice super-KdV equation
Adrian Stefan Carstea and Tomoyuki Takenawa,
J. Math. Phys., 60 (2019) ID 093503, 8pp

[26] An algebraically stable variety for a four-dimensional dynamical system reduced from the lattice super-KdV equation
Adrian Stefan Carstea and Tomoyuki Takenawa,
Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, 43--53,
Springer Proceedings in Mathematics & Statistics, 338, Springer, Cham., 2020

[27] Space of initial conditions for the four-dimensional Fuji-Suzuki-Tsuda system,
Tomoyuki Takenwa, RIMS Kokyuroku Bessatsu (in press), arXiv:2011.06271