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http://hdl.handle.net/1942/44445Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | De Maesschalck, Peter | - |
| dc.contributor.advisor | Huzak, Renato | - |
| dc.contributor.author | YEUNG, Melvin | - |
| dc.date.accessioned | 2024-10-08T12:55:54Z | - |
| dc.date.available | 2024-10-08T12:55:54Z | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-10-06T19:39:31Z | - |
| dc.identifier.uri | http://hdl.handle.net/1942/44445 | - |
| dc.description.abstract | This thesis is a combination of five chapters, all related to the Theorem of Dulac. Three chapters are dedicated to a dedicated analysis of the Finiteness proof of Ilyashenko, one is about maximal totally ordered sets in real analytic functions near infinity and the final chapter is a about a generalization of some aspects of D-modules and Differential Galois Theory to modules over Hopf module algebras. | - |
| dc.language.iso | en | - |
| dc.subject.other | PhD Thesis | - |
| dc.title | Transseries and superexact asymptotics in ordinary and partial differential equations | - |
| dc.type | Theses and Dissertations | - |
| local.bibliographicCitation.jcat | T1 | - |
| dc.relation.references | [1] L. V. Ahlfors. Remarks on Carleman’s formula for functions in a half-plane. SIAM Journal on Numerical Analysis, 3(2):183–187, 1966. [2] L.V. Ahlfors. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. International series in pure and applied mathematics. McGraw-Hill, 1966. [3] M. Aschenbrenner, L. van den Dries, and J. van der Hoeven. Asymptotic Differential Algebra and Model Theory of Transseries. Princeton University Press, 2017. [4] M. Aschenbrenner, L. van den Dries, and J. van der Hoeven. Maximal Hardy Fields. arXiv e-prints, page arXiv:2304.10846, April 2023. [5] W. Balser. From Divergent Power Series to Analytic Functions. Springer Berlin Heidelberg, 1994. [6] W. Balser. Formal power series and linear systems of meromorphic ordinary differential equations. Universitext. Springer-Verlag, New York, 2000. [7] A. Belotto da Silva, A. Figalli, A. Parusiński, and L. Rifford. Strong Sard conjecture and regularity of singular minimizing geodesics for analytic subriemannian structures in dimension 3. Invent. Math., 2022. cvgmt preprint. [8] I. Bendixson. Sur les courbes définies par des équations différentielles. Acta Mathematica, 24(none):1 – 88, 1901. [9] G. Binyamini, D. Novikov, and S. Yakovenko. On the number of zeros of Abelian integrals. Inventiones mathematicae, 181(2):227–289, Apr 2010. [10] F. Borceux. Handbook of Categorical Algebra, volume 2 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1994. [11] G. Böhm. Hopf Algebras and their Generalizations from a Category Theoretical Point of View. Lecture Notes in Mathematics. Springer International Publishing, January 2018. [12] H. Dulac. Sur les cycles limites. Bulletin de la Société Mathématique de France, 51:45–188, 1923. [13] F. Dumortier. Singularities of vector fields on the plane. Journal of Differential Equations, 23(1):53–106, 1977. [14] F. Dumortier, R. Roussarie, and C. Rousseau. Hilbert’s 16th problem for quadratic vector fields. Journal of Differential Equations, 110(1):86–133, 1994. [15] J. Ecalle. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Actualités mathématiques. Hermann, 1992. [16] Z. Galal, T. Kaiser, and P. Speissegger. Ilyashenko algebras based on transserial asymptotic expansions. Advances in Mathematics, 367:107095, 2020. [17] R. Godement. Topologie algébrique et théorie des faisceaux, volume No. 13 of Publications de l’Institut de Mathématiques de l’Université de Strasbourg [Publications of the Mathematical Institute of the University of Strasbourg]. Hermann, Paris, 1958. Actualités Scientifiques et Industrielles, No. 1252. [Current Scientific and Industrial Topics]. [18] Yu. S. Ilyashenko. Finiteness theorems for limit cycles. Lecture notes, in preparation. [19] Yu. S. Ilyashenko. Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane. Functional Analysis and Its Applications, 18(3):199–209, Jul 1984. [20] Yu. S. Ilyashenko. Dulac's memoir “on limit cycles” and related problems of the local theory of differential equations. Russian Mathematical Surveys, 40(6):1–49, dec 1985. [21] Yu. S. Ilyashenko. Separatrix lunes of analytic vector fields of the plane. Mosc. Univ. Math. Bull., 41(4):28–35, 1986. [22] Yu. S. Ilyashenko. Finiteness theorems for limit cycles, volume 94 of Translations of Mathematical Monographs. American Math. Society, 1991. [23] Yu. S. Ilyashenko, editor. Nonlinear Stokes phenomena. Advances in Soviet Mathematics 14. American Mathematical Society, Providence, 1993. [24] Yu. S. Ilyashenko. Nonlinear Stokes phenomena. In Nonlinear Stokes phenomena, volume 14 of Adv. Soviet Math., pages 1–55. Amer. Math. Soc., Providence, RI, 1993. [25] Yu. S. Ilyashenko. Centennial History of Hilbert’s 16th Problem. Bulletin of the American Mathematical Society, 39:301–354, 2002. [26] Yu. S. Ilyashenko and S. Yakovenko. Lectures on analytic differential equations. In Graduate Studies in Mathematics. American Mathematical Society, 2008. [27] T. Jech. Set Theory: The Third Millennium Edition, revised and expanded. Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2007. [28] Wilfred K. Approximation by entire functions. Michigan Mathematical Journal, 3(1):43 – 52, 1955. [29] T. Kaiser, J.-P. Rolin, and P. Speissegger. Transition maps at non-resonant hyperbolic singularities are o-minimal. Journal für die reine und angewandte Mathematik, 2009(636):1–45, 2009. [30] T. Kaiser and P. Speissegger. Analytic continuations of log-exp-analytic germs. Transactions of the American Mathematical Society, 371:5203–5246, 2019. [31] L. El Kaoutit and P. Saracco. The hopf algebroid structure of differentially recursive sequences. Quaestiones Mathematicae, 45(4):547–593, 2022. [32] M. Kashiwara and M. Saito. D-modules and Microlocal Calculus. Iwanami series in modern mathematics. American Mathematical Society, 2003. [33] E. R. Kolchin. Algebraic matric groups and the picard-vessiot theory of homogeneous linear ordinary differential equations. Annals of Mathematics, 49(1):1–42, 1948. [34] M. Loday-Richaud. Divergent series summability and resurgence II simple and multiple summability. Lecture Notes in Mathematics. Springer, Cham, 2016. [35] S. Majid. Foundations of Quantum Group Theory. Cambridge University Press, 1995. [36] J. Martinet and J.-P. Ramis. Problèmes de modules pour des équations différentielles non linéaires du premier ordre. Publications Mathématiques de l’IHÉS, 55:63–164, 1982. [37] S. Montgomery. Hopf Algebras and Their Actions on Rings. Number v. 82 in Hopf algebras and their actions on rings. American Mathematical Soc., 1993. [38] R. Moussu and C. Roche. Théorie de Hovanskii et problème de Dulac. Inventiones mathematicae, 105(2):431–442, 1991. [39] M.M. Peixoto. Structural stability on two-dimensional manifolds. Topology, 1(2):101–120, 1962. [40] D. Peran, M. Resman, J.P. Rolin, and T. Servi. Linearization of complex hyperbolic Dulac germs. Journal of Mathematical Analysis and Applications, 508(1):125833, 2022. [41] I. G. Petrovskij and E. M. Landis. On the number of limit cycles of the equation dy/dx = P(x, y)/Q(x, y), where p and q are polynomials of 2nd degree. Mat. Sb., Nov. Ser., 37:209–250, 1955. [42] E. Phragmén and E. Lindelöf. Sur une extension d’un principe classique de l’analyse et sur quelques propriétés des fonctions monogènes dans le voisinage d’un point singulier. Acta Math., 31(1):381–406, 1908. [43] H. Poincaré. Mémoire sur les courbes définies par une équation différentielle (ii). Journal de Mathématiques Pures et Appliquées, 8:251–296, 1882. [44] E.C. Titchmarsh. The theory of functions. University Press, Oxford, 2nd ed. edition, 1939. [45] H. Umemura. On the definition of the galois groupoid. Asterisque, 02 2009. [46] L. van den Dries, A. MacIntyre, and D. Marker. Logarithmic-exponential series. Annals of Pure and Applied Logic, 111(1):61–113, 2001. anayse logique. [47] F. Van Oystaeyen and Y. Zhang. Galois-type correspondences for Hopf Galois extensions. K-Theory, 8:257–269, 05 1994. [48] S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Texts in Applied Mathematics. Springer New York, 2003. | - |
| local.type.refereed | Non-Refereed | - |
| local.type.specified | Phd thesis | - |
| local.provider.type | - | |
| local.uhasselt.international | no | - |
| item.fullcitation | YEUNG, Melvin (2024) Transseries and superexact asymptotics in ordinary and partial differential equations. | - |
| item.fulltext | With Fulltext | - |
| item.accessRights | Embargoed Access | - |
| item.contributor | YEUNG, Melvin | - |
| item.embargoEndDate | 2029-10-08 | - |
| Appears in Collections: | Research publications | |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| a.pdf Until 2029-10-08 | Published version | 1.22 MB | Adobe PDF | View/Open Request a copy |
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