L. P. Shilnikov

Mathematics · Physical Sciences

30h-index3.7kcitations89works0.02yr avg
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Research Topics

Mathematical Dynamics and Fractals(43), Quantum chaos and dynamical systems(40), Nonlinear Dynamics and Pattern Formation(22), Advanced Differential Equations and Dynamical Systems(22), Chaos control and synchronization(21)

Publications87 total

Symbolic Dynamics in Multidimensional Annulus and Chimera States
International Journal of Bifurcation and Chaos·2014· 3 cited
Showcase of Blue Sky Catastrophes
International Journal of Bifurcation and Chaos·2014· 21 citedOpen Access
SYMBOLIC DYNAMICS AND SPIRAL STRUCTURES DUE TO THE SADDLE-FOCUS BIFURCATIONS
WORLD SCIENTIFIC eBooks·2013· 4 cited
Towards scenarios of chaos appearance in three-dimensional maps
Nelineinaya Dinamika·2012· 44 citedOpen Access
Romen Vasil'evich Plykin (obituary)
Russian Mathematical Surveys·2011
On a homoclinic origin of Hénon-like maps
Regular and Chaotic Dynamics·2010· 16 cited
On a homoclinic origin of Hénon-like maps
Regular and Chaotic Dynamics·2010
CENTER MANIFOLD.: NON-LOCAL CASE
World scientific series on nonlinear science, series A·2010
STRUCTURALLY STABLE EQUILIBRIUM STATES OF DYNAMICAL SYSTEMS
World scientific series on nonlinear science, series A·2010
CENTER MANIFOLD.: LOCAL CASE
World scientific series on nonlinear science, series A·2010· 1 cited
BASIC CONCEPTS
World scientific series on nonlinear science, series A·2010
INVARIANT TORI
World scientific series on nonlinear science, series A·2010
STRUCTURALLY STABLE PERIODIC TRAJECTORIES OF DYNAMICAL SYSTEMS
World scientific series on nonlinear science, series A·2010
On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
Regular and Chaotic Dynamics·2009· 42 cited
On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I
Nonlinearity·2008· 81 cited
Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors
Doklady Mathematics·2008· 53 cited
Shilnikov saddle-node bifurcation
Scholarpedia·2008· 4 citedOpen Access
On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index ½
Doklady Mathematics·2007· 7 cited
Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps
Nonlinearity·2007· 71 cited
Shilnikov bifurcation
Scholarpedia·2007· 35 citedOpen Access
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Frequent Co-authors

Dmitry Turaev(20), С. В. Гонченко(17), Andrey Shilnikov(8), Valentin Afraimovich(4), Leon O. Chua(3), В. В. Быков(2), I M Ovsyannikov(2), L. M. Lerman(2), V. S. Gonchenko(2), D. V. Turaev(1), A. S. Gonchenko(1), A. D. Morozov(1), O. V. Sten'kin(1), Yurij Neimark(1)