scholarly journals Homoclinic tangencies to resonant saddles and discrete Lorenz attractors

2017 ◽  
Vol 10 (2) ◽  
pp. 273-288 ◽  
Author(s):  
Sergey Gonchenko ◽  
◽  
Ivan Ovsyannikov ◽  
Keyword(s):  
Lorenz Attractors ◽  
Homoclinic Tangencies

scholarly journals Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

2014 ◽  
Vol 19 (4) ◽  
pp. 495-505 ◽  
Author(s):  
Sergey V. Gonchenko ◽  
Ivan I. Ovsyannikov ◽  
Joan C. Tatjer
Keyword(s):  
Saddle Points ◽  
Lorenz Attractors ◽  
Homoclinic Tangencies

CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS

1994 ◽  
Vol 04 (03) ◽  
pp. 489-519 ◽  
Author(s):  
LEONID P. SHIL’NIKOV
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Complex Dynamics ◽  
Multidimensional Systems ◽  
Chua’S Circuit ◽  
Rigorous Results ◽  
Chua's Circuit ◽  
Mathematical Problems ◽  
Homoclinic Tangencies

Mathematical problems arising from the study of complex dynamics in Chua’s circuit are discussed. An explanation of the extreme complexity of the structure of attractors of Chua’s circuit is given. This explanation is based upon recent results on systems with homoclinic tangencies. A number of new dynamical phenomena is predicted for those generalizations of Chua’s circuits which are described by multidimensional systems of ordinary differential equations.

scholarly journals On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies

2014 ◽  
Vol 19 (6) ◽  
pp. 702-717 ◽  
Author(s):  
Amadeu Delshams ◽  
Marina Gonchenko ◽  
Sergey V. Gonchenko
Keyword(s):  
Homoclinic Tangencies ◽  
Area Preserving

Persistent homoclinic tangencies for conservative maps near the identity

2000 ◽  
Vol 20 (2) ◽  
pp. 393-438 ◽  
Author(s):  
PEDRO DUARTE
Keyword(s):  
Hamiltonian Systems ◽  
Time Variable ◽  
Integrable Hamiltonian Systems ◽  
Homoclinic Tangencies

For families of conservative maps near the identity we prove the existence of open sets of parameters with persistence of homoclinic tangencies between stable and unstable leaves of ‘thick’ horse-shoes. Such families are obtained, for instance, by perturbing integrable Hamiltonian systems in $\mathbb{R}^2$ with a rapidly periodic oscillatory term and then performing a slowing change in the time variable.

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