Research and Papers

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2018N420

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1. Nonintegrability of Hamiltonian system perturbed from integrable system with two singular points, (submitted)
2. Monodromy of nonintegrable Hamiltonian system, (submitted)
3. Analytic continuation of Borel sum of formal solution of semilinear partial differential equation, (Accepted for publication in Asymptotic analysis) (2014)
4. Semi-formal solution and monodromy of some confluent hypergeometric equations, ( Accepted for publication in RIMS Kokyuroku Bessatsu) (2014)
5. (With Hiroshi Yamazawa) Borel summability of some semilinear system of partial differential equations, (Accepted for publications in Opuscula Mathematica.) (2014)
6. (With Yoshinari Tanaka) Global Properties of Evolutional Lotka-Volterra System, Advances in Pure Mathematics, Vol. 3, No. 9 (2013), 709-718.DOI: 10.4236/apm.2013.39097
7. Smooth-integrable and analytic- nonintegrable resonant Hamiltonians, RIMS Kokyuroku Bessatsu, B40, (2013), 177-189.
8. Asymptotic analysis to Goursat problems, RIMS Kokyuuroku Bessatsu, B37, (2013), 247-262.
9. Analytic- nonintegrable resonant Hamiltonians which are integrable in a sector, Proc. of Conf. ICFIDCAA 19,Tohoku University Press (2012), 85-96.
10. Summability of first integrals of a C^\omega-nonintegrable resonant Hamiltonian system, Banach Center Publ. 97, (2012), 169-178.
11. Sectorial solution to semilinear singular partial differential equation, manuscripta math., 137,441-455 (2012)
12. Asymptotic property of divergent formal solutions in linearization of singular vector field, Publications in RIMS, 47 Vol.4, (2011)
13. (With Werner Balser) Gevrey order of formal power series solutions of inhomogeneous partial differential equations with constant coefficients, Funkcial. Ekvac.,53 (2010),411-434.
14. (With Werner Balser) Integrability of Hamiltonian systems and transseries expansions, Accepted for publication in Math. Zeitschrift.
15. (With Yoshinari Tanaka) Predicting the phenotypic response of resource-competing communities to environmental change, Journal of Theoretical Biology, 257 (2009), 627-641
16. Analytic-Liouville-Nonintegrable Hamiltonian Systems, RIMS K\^oky\^uuroku Bessatsu, B10 (2008), 225-234.
17. (With A. Shirai) Singular solutions of nonlinear partial differential equations with resonances, J. Math. Soc. Japan, 60(1) (2008), 237-263.
18. (With T.Gramchev) Normal forms for commuting vector fields near a common fixed point, Proceedings of SPT 2007, World Scientific (2008), 81-91.
19. Analytic non-integrable Hamiltonian systems and irregular singularities, Annali di Matematica, 187, (2008), 555-562.
20. Divergence and resummation in the normal form theory of vector fields, RIMS K\^oky\^uuroku Bessatsu, B5 (2008), 113-119.
21. Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks, ANNALES DE L'INSTITUT FOURIER, 58 no. 1 (2008), 263-297 .
22. Convergent and divergent solutions of singular partial differential equations with resonance or small denominators, Publications of RIMS, Kyoto University, 43, (2007), 923-943.
23. WKB analysis and Poincar\'e theorem for vector fields, Proceeding of the Conference "Algebraic Analysis of Differential Equations" in honor of Prof. Kawai, Springer Verlag, (2007), 335-352.
24. Singular partial differential equations with resonance and small denominators, Proceeding of the Conference "Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and their Deformations. Painlev\'e Hierarchies" , RIMS K\^oky\^uuroku Bessatsu, B2 (2007), 261-265.
25. Finitely smooth solutions of nonlinear singular partial differential equations, Math. Nachr. 279, (No. 11) (2006), 1-22.
26. Diophantine phenomena in commuting vector fields and diffeomorphisms, Tsukuba J. Math. 28 (No.2) (2004), 389-399.
27. Riemann--Hilbert problem and solvability of differential equations, Rend. Sem. Mat. Univ. Pol. Torino 61 (2) (2003), 183-208.
28. Perturbations of vector fields on tori: resonant normal forms and diophantine phenomena, Proc. Edinburgh Math. Soc. (2002), 45, 731-759.
29. Global solvability of Monge-Amp\`ere type equations, Comm. Partial Differential Equations, 25 (2000), 1925-1950.
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