Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
---|---|---|
Page(s) | 71 - 83 | |
DOI | https://doi.org/10.1051/mmnp/20138505 | |
Published online | 17 September 2013 |
- S.V. Gonchenko, O.V. Sten’kin, L.P. Shilnikov. On existence of infinitely many stable and unstable invariant tori for systems from newhouse regions with heteroclinic tangencies. Rus. Nonlinear Dynamics, 2 (2006), 3–25. [Google Scholar]
- N.K. Gavrilov. On three-dimensional dynamical systems having a structurally unstable homoclinic contour. Rus. Math. Notes, 14 (1973), 687–696. [CrossRef] [Google Scholar]
- N.K. Gavrilov, L.P. Shilnikov. On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I. Math. USSR Sbornik, 17 (1972), 467–485; II. Math. USSR Sbornik, 19 (1973), 139–156. [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. On Newhouse regions of two-dimensional diffeomorphisms close to a diffeomorphism with a nontransversal heteroclinic cycle. Proc. Steklov Inst. Math. 216 (1997), 70–118. [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, O.V. Stenkin. On Newhouse regions with infinitely many stable and unstable invariant tori. Proceedings of the Int. Conf. “Progress in Nonlinear Science” dedicated to 100th Anniversary of A.A. Andronov, July 2-6; v. 1 “Mathematical Problems of Nonlinear Dynamics”, Nizhny Novgorod (2002) 80–102. [Google Scholar]
- S. Gonchenko, L. Shilnikov, D. Turaev. Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Nonlinearity, 20 (2007), 241–275. [CrossRef] [MathSciNet] [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. On dynamical properties of multidimensional diffeomorphisms from Newhouse regions. I. Nonlinearity, 21 (2008), 923–972. [CrossRef] [Google Scholar]
- J.S.W. Lamb, O.V. Sten’kin. Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits. Nonlinearity, 17 (2004), 1217–1244. [CrossRef] [MathSciNet] [Google Scholar]
- A. Delshams, S.V. Gonchenko, V.S. Gonchenko, J.T. Lazaro, O. Sten’kin. Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps. Nonlinearity, 26 (2013), 1–33. [CrossRef] [MathSciNet] [Google Scholar]
- S.V. Gonchenko, A.S. Gonchenko, A.O. Kazakov. On new aspects of chaotic dynamics of “celtic stone”. Rus. Nonlinear Dynamics, 8 (2013), 507–518. [Google Scholar]
- D.V. Turaev. On dimension of non-local bifurcational problems. Bifurcation and Chaos, 6 (1996), 919–948. [CrossRef] [Google Scholar]
- S.V. Gonchenko, L. Shilnikov, D. Turaev. On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Regul. Chaotic Dyn., 14 (2009), 137–147. [CrossRef] [MathSciNet] [Google Scholar]
- S.V. Gonchenko, I.I. Ovsyannikov, C. Simó, D. Turaev. Three-dimensional Hénon-like maps and wild Lorenz-like attractors. Bifurc. Chaos, 15 (2005), 3493–3508. [Google Scholar]
- S.V. Gonchenko, J.D. Meiss, I.I. Ovsyannikov. Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation. Regular Chaotic Dyn., 11 (2006), 191–212. [Google Scholar]
- D.V. Turaev, L.P. Shilnikov. An example of a wild strange attractor. Sbornik Mathematics, 189 (1998), 137–160. [Google Scholar]
- D.V. Turaev, L.P. Shilnikov. Pseudo-hyperbolisity and the problem on periodic perturbations of Lorenz-like attractors. Russian Dokl. Math., 77 (2008), 17–21. [CrossRef] [Google Scholar]
- S.V. Gonchenko, A.S. Gonchenko, I.I. Ovsyannikov, D.V. Turaev. Examples of Lorenz-like attractors in Hénon-like maps. Math. Model. Nat. Phenom. 8 (2013), 32–54. [Google Scholar]
- L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, L.O. Chua. Methods of qualitative theory in nonlinear dynamics. Part I, World Scientific, 1998. [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov. Invariants of ??-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory. Ukrainian Mathematical Journal, 42 (1990), 134–140. [CrossRef] [MathSciNet] [Google Scholar]
- S.V. Gonchenko. Dynamics and moduli of Ω-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point. AMS Transl. Math., 200 (2000), 107–134. [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. On the existence of Newhouse regions near systems with non-rough Poincare homoclinic curve (multidimensional case). Russian Acad. Sci. Dokl. Math., 47 (1993), 268–283. [MathSciNet] [Google Scholar]
- A.L. Shilnikov, L.P. Shilnikov, D.V. Turaev. Normal forms and Lorenz attractors. Bifurc. Chaos, 3 (1993), 1123–1139. [Google Scholar]
- A.L. Shilnikov. Bifurcation and chaos in the Marioka-Shimizu system. Methods of qualitative theory of differential equations, Gorky (1986), 180–193 [English translation in Selecta Math. Soviet., 10 (1991), 105–117] [Google Scholar]
- A.L. Shilnikov. On bifurcations of the Lorenz attractor in the Shimuizu-Morioka model. Physica D, 62 (1993), 338–346. [CrossRef] [Google Scholar]
- G. Tigan, D. Turaev. Analytical search for homoclinic bifurcations in the Shimizu-Morioka model. Physica D: Nonlinear Phenomena, 240 (2011), 985–989. [CrossRef] [Google Scholar]
- Homoclinic tangencies, edited by S.V. Gonchenko and L.P. Shilnikov, Moscow-Izhevsk, 2007. [Google Scholar]
- S.V. Gonchenko, V.S. Gonchenko, L.P. Shilnikov. On homoclinic origin of Henon-like maps. Regular and Chaotic Dynamics, 4–5 (2010), 462–481. [Google Scholar]
- S.V. Gonchenko, I.I. Ovsyannikov, D.V. Turaev. On the effect of invisibility of stable periodic orbits at homoclinic bifurcations. Physica D, 241 (2012), 1115–1122. [CrossRef] [Google Scholar]
- V. Rom-Kedar, D. Turaev. Big islands in dispersing billiard-like potential. Physica D, 130 (1999), 187–210. [Google Scholar]
- S.V. Gonchenko, V.S. Gonchenko. On bifurcations of the birth of closed invariant curves in the case of two-dimensional diffeomorphisms with homoclinic tangencies. Proc. Steklov Inst. Math., 244 (2004), 80–105. [Google Scholar]
- S.V. Gonchenko, D.V. Turaev, L.P. Shilnikov. Dynamical phenomena in multi-dimensional systems with a non-rough Poincare homoclinic curve. Russ. Acad. Sci. Dokl. Math., 47 (1993), 410–415. [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits. Chaos, 6 (1996), 15–31. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. On dynamical properties of diffeomorphisms with homoclinic tangencies. J. Math. Sci., 126 (2005), 1317–1343. [MathSciNet] [Google Scholar]
- S.V. Gonchenko, V.S. Gonchenko, J.C. Tatjer. Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps. Regular and Chaotic Dynamics, 12 (2007), 233–266. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.