Pokaż uproszczony rekord

dc.contributor.authorZieliński, Janusz
dc.contributor.editorKrasiński, Tadeusz
dc.contributor.editorSpodzieja, Stanisław
dc.date.accessioned2020-01-28T12:30:18Z
dc.date.available2020-01-28T12:30:18Z
dc.date.issued2019
dc.identifier.citationZieliński J., Rings and fields of constants of cyclic factorizable derivations, in: Analytic and Algebraic Geometry 3, T. Krasiński, S. Spodzieja (red.), WUŁ, Łódź 2019, doi: 10.18778/8142-814-9.16.pl_PL
dc.identifier.isbn978-83-8142-814-9
dc.identifier.urihttp://hdl.handle.net/11089/31347
dc.description.abstractWe present a survey of the research on rings of polynomial constants and fields of rational constants of cyclic factorizable derivations in polynomial rings over fields of characteristic zero.pl_PL
dc.language.isoenpl_PL
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl_PL
dc.relation.ispartofAnalytic and Algebraic Geometry 3;
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleRings and fields of constants of cyclic factorizable derivationspl_PL
dc.typeBook chapterpl_PL
dc.page.number213-226pl_PL
dc.contributor.authorAffiliationNicolaus Copernicus University, Faculty of Mathematics and Computer Sciencepl_PL
dc.identifier.eisbn978-83-8142-815-6
dc.referencesM. A. Almeida, M. E. Magalh~aes, I. C. Moreira, Lie symmetries and invariants of the Lotka- Volterra system, J. Math. Phys. 36 (1995), 1854-1867.pl_PL
dc.referencesO. I. Bogoyavlenski , Algebraic constructions of integrable dynamical systems - extension of the Volterra system, Russian Math. Surveys 46 (1991), 1-64.pl_PL
dc.referencesF. H. Busse, Transitions to Turbulence Via the Statistical Limit Cycle Route, Synergetics, Springer-Verlag, Berlin 1978.pl_PL
dc.referencesL. Cairó, Darboux First Integral Conditions and Integrability of the 3D Lotka-Volterra Sys- tem, J. Nonlinear Math. Phys. 7 (2000), 511-531.pl_PL
dc.referencesL. Cairó, J. Llibre, Darboux integrability for 3D Lotka-Volterra systems, J. Phys. A 33 (2000), 2395{2406.pl_PL
dc.referencesA. van den Essen, Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, 190. Birkh auser Verlag, Basel 2000.pl_PL
dc.referencesP. Heged}us, The constants of the Volterra derivation, Cent. Eur. J. Math. 10 (2012), 969-973.pl_PL
dc.referencesP. Heged}us, J. Zieliński, The constants of Lotka-Volterra derivations, Eur. J. Math. 2 (2016), 544-564.pl_PL
dc.referencesY. Itoh, Integrals of a Lotka-Volterra System of Odd Number of Variables, Progr. Theoret. Phys. 78 (1987), 507-510.pl_PL
dc.referencesS. Kuroda, Fields de ned by locally nilpotent derivations and monomials, J. Algebra 293 (2005), 395-406.pl_PL
dc.referencesS. Labrunie, On the polynomial rst integrals of the (a; b; c) Lotka{Volterra system, J. Math. Phys. 37 (1996), 5539-5550.pl_PL
dc.referencesW. E. Lamb, Theory of an Optical Maser, Phys Rev. A 134 (1964), 1429.pl_PL
dc.referencesG. Laval, R. Pellat, Plasma Physics, Proceedings of Summer School of Theoretical Physics, Gordon and Breach, New York 1975.pl_PL
dc.referencesA. J. Lotka, Analytical Note on Certain Rhythmic Relations in Organic Systems, Proc. Natl. Acad. Sci. U.S. 6 (1920), 410-415.pl_PL
dc.referencesR. Lupini, G. Spiga, Chaotic Dynamics of Spatially Homogeneous Gas Mixtures, Phys. Fluids. 31 (1988), 2048-2051.pl_PL
dc.referencesA. J. Maciejewski, J. Moulin Ollagnier, A. Nowicki, J.-M. Strelcyn, Around Jouanolou non- integrability theorem, Indag. Math. (N.S.) 11 (2000), 239-254.pl_PL
dc.referencesJ. Moulin Ollagnier, Liouvillian rst integrals of homogeneous polynomial 3-dimensional vector elds, Colloq. Math. 70 (1996), 195-217.pl_PL
dc.referencesJ. Moulin Ollagnier, Polynomial rst integrals of the Lotka-Volterra system, Bull. Sci. Math. 121 (1997), 463-476.pl_PL
dc.referencesJ. Moulin Ollagnier, Rational integration of the Lotka-Volterra system, Bull. Sci. Math. 123 (1999), 437-466.pl_PL
dc.referencesJ. Moulin Ollagnier, A. Nowicki, Polynomial algebra of constants of the Lotka-Volterra sys- tem, Colloq. Math. 81 (1999), 263-270.pl_PL
dc.referencesJ. Moulin Ollagnier, A. Nowicki, Constants of cyclotomic derivations, J. Algebra 394 (2013), 92-119.pl_PL
dc.referencesV. W. Noonburg, A Neural Network Modeled by an Adaptive Lotka-Volterra System, SIAM J. Appl. Math. 49 (1989), 1779-1792.pl_PL
dc.referencesA. Nowicki, Commutative bases of derivations in polynomial and power series rings, J. Pure Appl. Algebra 40 (1986), 275-279.pl_PL
dc.referencesA. Nowicki, Polynomial derivations and their rings of constants, Nicolaus Copernicus University, Toruń 1994.pl_PL
dc.referencesA. Nowicki, J. Zieliński, Rational constants of monomial derivations, J. of Algebra 302 (2006), 387-418.pl_PL
dc.referencesP. Ossowski, J. Zieliński, Polynomial algebra of constants of the four variable Lotka-Volterra system, Colloq. Math. 120 (2010), 299-309.pl_PL
dc.referencesV. Volterra, Le cons sur la Th eorie Math ematique de la Lutte pour la vie, Gauthier Villars, Paris 1931.pl_PL
dc.referencesJ. Zieliński, The ve-variable Volterra system, Cent. Eur. J. Math. 9 (2011), 888-896.pl_PL
dc.referencesJ. Zieliński, Rings of constants of four-variable Lotka-Volterra systems, Cent. Eur. J. Math. 11 (2013), 1923-1931.pl_PL
dc.referencesJ. Zieliński, The eld of rational constants of the Volterra derivation, Proc. Est. Acad. Sci. 63 (2014), 133-135.pl_PL
dc.referencesJ. Zieliński, Rational constants of generic LV derivations and of monomial derivations, Bull. Pol. Acad. Sci. Math. 61 (2013), 201-208.pl_PL
dc.referencesJ. Zieliński, Fields of rational constants of cyclic factorizable derivations, Electron. J. Differential Equations 2015 (2015), 1-7.pl_PL
dc.referencesJ. Zieliński, P. Ossowski, Rings of constants of generic 4D Lotka-Volterra systems, Czechoslovak Math. J. 63 (2013), 529-538.pl_PL
dc.referencesH. Żołądek, Multi-dimensional Jouanolou system, J. Reine Angew. Math. 556 (2003), 47-{78.pl_PL
dc.contributor.authorEmailubukrool@mat.uni.torun.plpl_PL
dc.identifier.doi10.18778/8142-814-9.16


Pliki tej pozycji

Thumbnail
Thumbnail
Thumbnail

Pozycja umieszczona jest w następujących kolekcjach

Pokaż uproszczony rekord

Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe