Differential equations and Integrability. Three-body problem.

[1] A. Tsygvintsev, Velocity Syzygies and Bounding Syzygy Moments in the Planar Three-Body Problem, C.R. Acad. Sci. Paris, to appear, 2024

[2] A. Tsygvintsev, On some collinear configurations  in the planar three-body problem, Nonlinearity 36 6827, 2023, Arxiv  

[3] A. Tsygvintsev, On the existence of generalised  syzygies in the planar three-body problem, C.R. Acad. Sci. Paris, vol 361, 331-335, 2023, link

[4] A. Tsygvintsev, H. Dullin, On the analytic non-integrability of the Rattleback problem, Annales de la faculté des sciences de Toulouse, Vol. XVII,   n. 3, pp. 495-517, 2008

[5] A. Tsygvintsev, On some exceptional cases in the integrability of the three-body problem, Celestial Mechanics and Dynamical Astronomy, Vol. 99, No. 1, 237-247, 2007

[6] A. Tsygvintsev, Non-existence of new meromorphic first integrals in the planar three-body problem, Celestial Mech. Dynam. Astronom. 86 (2003), no. 3, 237-247

[7] A. Tsygvintsev, The meromorphic non-integrability of the three-body problem, Journal für die Reine und Angewandte Mathematik de Gruyter (Crelle's journal), N 537, 2001, 127-149

[8] A. Tsygvintsev, Sur l'absence d'une intégrale première supplémentaire méromorphe dans le problème plan des trois corps, C.R. Acad. Sci. Paris, t. 333, Série I, p. 125-128, 2001

[9] A. Tsygvintsev, On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations, J. Phys. A: Math. Gen. 34 (2001) 2185-2193

[10] A. Tsygvintsev, Algebraic invariant curves of plane polynomial differential systems, J. Phys. A: Math. Gen. 34 (2001) 663-672

[11] A. Tsygvintsev, La non-intégrabilité méromorphe du problème plan des trois corps, C.R. Acad. Sci. Paris, t. 331, Série I, p. 241-244, 2000

[12] K. Emelyanov, A. Tsygvintsev, Kovalevskaya exponents of the systems with the exponential interaction, Russian Acad. Sci. Sb. Math., T. 191, No. 10, p. 39-50, 2000

[13] A. Tsygvintsev, Sur l'intégrabilité algébrique d'un système d'équations différentielles dérivé des équations d'Euler sur l'algèbre so(4), Bull. Sci. math., Vol. 123, no. 8, p. 665-670, 1999

[14] A. Tsygvintsev, A. Borisov, Kovalevskaya's method in the dynamics of a rigid body, J. Appl. Math. Mech. 61, no. 1, p. 27-32, 1997

[15] A. Tsygvintsev, A. Borisov, Kovalevskaya exponents and integrable systems of classical dynamics I, II, Regular and Chaotic dynamics 1, no. 1, p. 15-28, 29-37, 1996

Analytic theory of continued fractions

[16] A. Tsygvintsev, Bounded analytic maps, Wall fractions and ABC flow, Journal of Approximation  Theory, 174, 206–219, 2013

[17] A. Tsygvintsev, Continued g-fractions and geometry of bounded analytic maps, Journal of Dynamical and Control Systems, Vol 19, No. 14, 2013

[18] A. Tsygvintsev, On the convergence of continued fractions at Runckel's points, The Ramanujan Journal, Vol. 15,  No.  3,  407-413, 2008

Mathematical Biology

[19]  A. Tsygvintsev, On the global attractors in one mathematical model of antiviral immunity, Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1199-1205, link
[20]  A. Tsygvintsev, L'immunité antivirale : la guerre invisible à la loupe des mathématiciens, Images des Mathématiques CNRS, 2020, link

[21] A. Tsygvintsev, Evolutionary paradigm in cancer immunology, ESAIM: Proceedings and Surveys, Vol. 45, p. 285-289, 2014

[22] A. Tsygvintsev, D. Kirschner,  S. Marino, A mathematical model of Gene Therapy for the Treatment of Cancer, in the book  "Mathematical Models and Methods in Biomedicine" (eds. U. Ledzewicz, Friedman, E. Kashdan, H. Schaettler), 2012, Springer-Verlag, Berlin

[23] D. Kirschner, A. Tsygvintsev, On the global dynamics of a model for  tumor immunotherapy, Journal of Mathematical Biosciences and Engineering Volume 6(3), pp 573-583, 2009

[24] A. Tsygvintsev, S. Banerjee, Bounded immune response in immunotherapy described by deterministic delay Kirschner-Panetta model, Applied Mathematical Letters, vol. 35, pp. 90-94, 2014

[25]  S. Banerjee, A. Tsygvintsev, Stability and bifurcations of equilibria  in a delayed Kirschner-Panetta model, Applied Mathematical Letters, Vol 40, pp. 65-71, 2015

 

Renormalization theory, holomorphic dynamics

[26] A. Singh, A. Tsygvintsev, On Julia Set Of Permutable Transcendental Entire Functions, Journal of the Calcutta Mathematical Society,Vol.6 No.2, 2010

[27] B. D. Mestel, A. Osbaldestin, A. Tsygvintsev, Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling, Communications in Mathematical Physics, Volume 250, Number 2, 241-257, 2004

[28] A. Tsygvintsev, On the connection between g-fractions and solutions of the Feigenbaum-Cvitanovic equation, Commun. in the Analytic Theory of Continued Fractions, Vol. XI, 2003, 103-112

[29] A. Tsygvintsev, B. D. Mestel, A. Osbaldestin, Continued fractions and solutions of the Feigenbaum-Cvitanovic equation, C.R. Acad. Sci. Paris, t. 334, Série I, p. 683-688, 2002

Artifitial Neural Networks & Deep Learning

[30] A. Tsygvintsev, On the overfly algorithm in  deep learning of neural networks, Applied Mathematics and Computation, 349 (2019) 348–358, download from arXiv

[31] A. Tsygvintsev,  Natural  vs. random protein sequences - the novel neural network approach based on time series analysis,   Journal of Proteins and Proteomics, 11:11–16, 2020
       View only version can be found here                         

History of Mathematics

[32] J.-M. Strelcyn A. Tsygvintsev, Poincaré theorems, Encyclopedia of Nonlinear Science, ed. Alwyn Scott. New York and London: Routledge, 2004

Popularization of Mathematics

[33] L. Lazrag et A. Tsygvintsev, L’anagyre. Un objet curieux..., Images des Mathématiques CNRS, link

[34] Participation in French TV show "Magique ou scientifique ?" of a television network France 5. link video.

The reviews on MathSciNet of my papers can be found here    (access to mathscinet is required)

The reviews on MathSciNet written by me can be found here   

ORCID iD iconhttps://orcid.org/0000-0002-8744-4100