D.Turaev, Richness of chaos in the absolute Newhouse domain, in Proc. ICM 2010, vol.3 (Hindustan Book Agency, 2010) 1804-1815
D.Turaev, On dimension of non-local bifurcational problems, Bifurcation and Chaos 6, 919-948 (1996)
| Short announcement: On dimension reduction near homoclinic and heteroclinic cycles, J. Techn. Phys. 37, 374-377 (1996) |
S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps, Nonlinearity 20, 241-275 (2007)
| Short version: Homoclinic tangencies of arbitrarily high orders in conservative two-dimensional maps, Doclady Math. 73, 210-213 (2006) | ||
| D.Turaev, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, Ergod. Th. & Dynam. Sys. 31, 563-569 (2011) | |
| D.Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in nonhyperbolic area-preserving maps, Nonlinearity 16, 1-13 (2003) | |
| V.Gelfreich, D.Turaev, Universal dynamics in a neighbourhood of a generic elliptic periodic point, Regul. Chaotic Dyn. 15,159-164 (2010) | |
S.V.Gonchenko,L.P.Shilnikov, D.Turaev, On models with non-rough Poincare homoclinic curves , Physica D 62, 1-14 (1993)
| Russian version: On models with non-rough Poincare homoclinic curves, Methods of qualitative theory and theory of bifurcations, 36-61 (1991) | |
| Short version: | On models with a structurally unstable Poincare homoclinic curve, Sov. Math., Dokl. 44, 422-426 (1992) |
| Detailed proofs: | Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, J. Math. Sci 105, 1738-1778 (2001) |
| Russian version: Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, in Contemporary Mathematics and its Applications 67 (VINITI, Moscow, 1999) | |
S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On the existence of Newhouse domains in a neighborhood of systems with a structurally unstable Poincare homoclinic curve (the higher-dimensional case), Russian Acad. Sci., Dokl., Math. 47, 268-273 (1993)
S.V.Gonchenko, D.Turaev, L.P.Shilnikov, Dynamical phenomena in multi-dimensional systems with a structurally unstable Poincare homoclinic curve, Russian Acad. Sci., Dokl., Math. 47, 410-415 (1993)
S.V.Gonchenko, L.Shilnikov, D.Turaev, On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I, Nonlinearity 21 (2008)
| Basic (partial) cases: On dynamical properties of diffeomorphisms with homoclinic tangencies, J. Math. Sci. 126, 1317-1343 (2005) |
| Russian version: On dynamical properties of diffeomorphisms with homoclinic tangencies, Sovrem. Mat. Prilozh. 7, 91-117 (2003) | ||
| Conference proceedings: On dynamical properties of diffeomorphisms with homoclinic tangencies, in Proc. Symposium Henrie Poincare, 41-72 (Solvay Inst., 2005) | ||
| S.V.Gonchenko, I.I.Ovsyannikov, D.Turaev, On the effect of invisibility of stable periodic orbits at homoclinic bifurcations, Physica D 241, 1115-1122 (2012) | |
S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On Newhouse domains of two-dimensional diffeomorphisms with a structurally unstable heteroclinic cycle, Proc. Steklov Inst. Math. 216, 76-125 (1997)
| Short announcement: Bifurcations of two-dimensional diffeomorphisms with non-rough homoclinic contours, J. Techn. Phys. 37, 349-352 (1996) | |
| S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regul. Chaotic Dyn. 3, 3-26 (1998) |
| S.V.Gonchenko, D.V.Turaev, L.P.Shilnikov, Infinitely many elliptic periodic orbits in four-dimensional symplectic diffeomorphisms with a homoclinic tangency, Proc. Steklov Inst. Math. 244, 106-131 (2004) |
S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits, Chaos 6, 15-31 (1996)
| Conference proceedings: Quasiattractors and homoclinic tangencies, Comput. Math. Appl. 34, 195-227 (1997) |
| S.V.Gonchenko, O.Sten'kin, D.Turaev, Complexity of homoclinic bifurcations and Ω-moduli , Bifurcation and Chaos 6, 969-989 (1996) |
| P.Gaspard, S.Gonchenko, G.Nicolis, D.Turaev, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, Nonlinearity 10, 409-423 (1997) |
| Conference proceedings: S.V.Gonchenko, L.P.Shilnikov, O.Sten'kin, D.Turaev, Dynamical systems with structurally unstable homoclinic orbits and moduli of Ω-equivalence, Comput. Math. Appl. 34 (1997) |
Wild attractors
S.V.Gonchenko, L.Shilnikov, D.Turaev, On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors, Regul. Chaotic Dyn. 14, 137-147 (2009)
D.Turaev, L.Shilnikov, Pseudohyperbolicity and the problem of periodic perturbation of Lorenz-like attractors, Doklady Math. 77 (2008)
S.V.Gonchenko, I.I.Ovsyannikov, C.Simo, D.Turaev, Three-dimensional Henon-like map and wild Lorenz-like attractors, Bifurcation and Chaos 15, 3493-3508 (2005)
D.Turaev, L.P.Shilnikov, An example of a wild strange attractor, Sb. Math. 189, 137-160 (1998)
Examples
D.Turaev, V.Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 575-599 (1998)
A.Dmitriev, Yu.Komlev, D.Turaev, Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol - Duffing equation, Bifurcation and Chaos 2, 93-100 (1992)
V.Biragov, I.M.Ovsyannikov, D.Turaev, A study of one endomorphism of a plane, Methods of qualitative theory and theory of bifurcations, 72-86 (1988)
D.Turaev, L.P.Shilnikov, Bifurcations of quasiattractors torus-chaos, in "Mathematical mechanisms of turbulence," 113-121 (Kiev, 1986)
