My area is Dynamical Systems. My research interests lie in the study of homoclinic orbits in conservative dynamical systems, namely, homoclinic bifurcations in area-preserving and reversible maps, splitting of separatrices in Hamiltonian systems, hyperbolic invariant tori with several frequencies, systems with parabolic points, billiard systems, with special attention to models coming from Classical and Celestial Mechanics.

CV (updated March 2021)

1. Scientific paper. J. Torrents, V. Dunjko, M. Gonchenko, G. E. Astrakharchik, M. Olshanii (2022). The origin of the period-2T/7 quasi-breathing in disk-shaped Gross-Pitaevskii breathers. SciPost Phys. 12, 092 

2. Scientific paper. M. S. Gonchenko, A. O. Kazakov, E. A. Samylina, A. I. Shykhmamedov. On 1:3 resonance under reversible perturbations of conservative cubic Hénon maps (2022). Regul. Chaotic Dyn., 27 (2):198-216. arXiv:2105.01360. 

3. Scientific paper. M.  Olshanii, D. Deshommes, J. Torrents, M. Gonchenko, V. Dunjko, G. E. Astrakharchik (2021). Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves. SciPost Phys., 10, 114. 

4.  Scientific paper. A. Gonchenko, M. Gonchenko, A. Kozlov, E. Samylina (2021). On scenarios of homoclinic attractors onset in three-dimensional non-orientable maps. Chaos, 31(4):043122 [18pp].

5. Scientific paper. M. Gonchenko, S.V. Gonchenko, K. Safonov (2021). Reversible perturbations of conservative Henon-like maps. Discrete Contin. Dyn. Syst.,  41(4): 1875-1895. 

6. Scientific paper. A. Delshams, M. Gonchenko, P. Gutiérrez (2020). Exponentially Small Splitting of Separatrices Associated to 3D Whiskered Tori with Cubic Frequencies. Comm. Math. Phys., 378(3):1931-1976.

7. Scientific paper. X. Aretxabaleta, M. Gonchenko, N. Harshman, S, Jackson, M. Olshanii, G. Astrakharchik (2020). The Dynamics of Digits: Calculating Pi with Galperin’s Billiards. Mathematics. 8(4):509, pp. 1-31.

8. Scientific paper. S. V. Gonchenko, M. Gonchenko, I. O. Sinitsky (2020). On the mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric heteroclinic contours. Izv. Ross. Akad. Nauk Ser. Mat., 84(1):23-51.

9. Scientific paper. M. Gonchenko, S. Gonchenko, I. Ovsyannikov, A. Vieiro (2018). On local and global aspects of 1:4 resonance in the cubic Hénon maps. Chaos, 28(4):043123 [15 pp].

10. Scientific paper. A. Delshams, M. Gonchenko, S.V. Gonchenko, J.T. Lázaro (2018). Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies. Discrete Contin. Dyn. Syst., 38(9): 4483-4507.

11. Scientific paper. M. Gonchenko, S. Gonchenko, I. Ovsyannikov (2017). Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. Math. Model. Nat. Phenom., 12(1): 41-61.

12. Scientific paper. A. Delshams, M. Gonchenko, P. Gutiérrez (2016). Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio. SIAM J. Appl. Dyn. Syst.,15(2):981–1024.

13. Book Chapter. A. Delshams, M. Gonchenko, S. Gonchenko (2016). On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds. Difference equations, discrete dynamical systems and applications, Springer Proc. Math. Stat. [edited by Ll. Alsedà et al.].180:107-125. Springer-Verlag Berlin Heidelberg.

14. Scientific paper. A.Delshams, M.Gonchenko, S.Gonchenko (2015).On dynamics and bifurcations of area-preserving maps with homoclinic tangencies. Nonlinearity, 28(9):3027-3071.

15. Book Chapter. A. Delshams, M. Gonchenko, P. Gutiérrez (2015). A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies. Extended Abstracts Spring 2014: Hamiltonian Systems and Celestial Mechanics, Trends Math. Res. Perspect. CRM Barc. [edited by Corbera et al.]. 4:31-37. Birkhäuser Basel.

16. Scientific paper. A. Delshams, M. Gonchenko, S. Gonchenko (2014). On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies. Regul. Chaotic Dyn., 19(6):702-717.

17. Scientific paper. A. Delshams, M. Gonchenko, P. Gutiérrez (2014). Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio. Regul. Chaotic Dyn., 19(6):663-680.

18. Scientific paper. A. Delshams, M. Gonchenko, P. Gutiérrez (2014). Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type. Internat. J. Bif. Chaos, 24(8):1440011 [12 pp].

19. Scientific paper. A. Delshams, M. Gonchenko, P. Gutiérrez (2014). Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies. Electron. Res. Announc. Math. Sci., 21:41-61.

20. Scientific paper. M. Gonchenko, S. Gonchenko (2009). On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies, Regul. Chaotic Dyn., 14(1):116-136.

21. Scientific paper. M. S. Gonchenko (2005). On the structure of 1:4 resonances in Hénon maps. Internat. J. Bif. Chaos, 15(11):3653-3660.

22. Book Chapter. M. Gonchenko (2003). A comparison analysis of bifurcations in standard and generalized Hénon maps. Proc. N.Novgorod Univ. [edited by V.Saveliev et al.], 104-106.