01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
Keywords:
chaos, homoclinic bifurcations, Lorenz attractor
UDC:
517.9
Subject:
homoclinic bifurcations, Henon map
Main publications:
Gonchenko S.V., Ovsyannikov I.I., Simo C., Turaev D.V., “Three-dimensional Henon maps and wild Lorenz-type strange attractors.”, International Journal of Bifurcation and Chaos, 15:11 (2005), 3493-3508
Gonchenko S.V., Meiss J.D., Ovsyannikov I.I., “Chaotic dynamics of three-dimensional Henon maps that originate from a homoclinic bifurcation.”, Regular and Chaotic Dynamics, 11 (2006), 191-212
S.V. Gonchenko, I.I. Ovsyannikov, D. Turaev, “On the effect of invisibility of stable periodic orbits at homoclinic bifurcations”, Physica D: Nonlinear Phenomena, 241:13 (2012), 1115-1122
Ivan I. Ovsyannikov, “On the Birth of Discrete Lorenz Attractors
Under Bifurcations of 3D Maps
with Nontransversal Heteroclinic Cycles”, Regul. Chaotic Dyn., 27:2 (2022), 217–231
2015
2.
I. Ovsyannikov, D. Turaev, S. Zelik, “Bifurcation to chaos in the ñomplex Ginzburg–Landau equation with large third-order dispersion”, Model. Anal. Inform. Sist., 22:3 (2015), 327–336
Sergey V. Gonchenko, Ivan I. Ovsyannikov, Joan C. Tatjer, “Birth of Discrete Lorenz Attractors at the Bifurcations of 3D Maps with Homoclinic Tangencies to Saddle Points”, Regul. Chaotic Dyn., 19:4 (2014), 495–505
Sergey V. Gonchenko, Îlga V. Gordeeva, Valery I. Lukyanov, Ivan I. Ovsyannikov, “On Bifurcations of Multidimensional Diffeomorphisms Having a Homoclinic Tangency to a Saddle-node”, Regul. Chaotic Dyn., 19:4 (2014), 461–473
I. I. Ovsyannikov, “On stability of the Chaplygin ball motion on a plane with an arbitrary friction law”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 4, 140–145
S. V. Gonchenko, I. I. Ovsyannikov, “On bifurcations of three-dimensional diffeomorphisms with a non-transversal heteroclinic cycle containing saddle-foci”, Nelin. Dinam., 6:1 (2010), 61–77
S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov, “Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation”, Regul. Chaotic Dyn., 11:2 (2006), 191–212
V. S. Gonchenko, I. I. Ovsyannikov, “On bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a “neutral” saddle fixed point”, Zap. Nauchn. Sem. POMI, 300 (2003), 167–172; J. Math. Sci. (N. Y.), 128:2 (2005), 2774–2777
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