scholarly journals Persistence of homoclinic tangencies for area-preserving maps

1997 ◽  
Vol 6 (4) ◽  
pp. 711-725 ◽  
Author(s):  
Leonardo Mora ◽  
Neptalí Romero
Keyword(s):  
Area Preserving Maps ◽  
Homoclinic Tangencies ◽  
Area Preserving

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

Nonlinearity ◽  
2015 ◽  
Vol 28 (9) ◽  
pp. 3027-3071 ◽  
Author(s):  
Amadeu Delshams ◽  
Marina Gonchenko ◽  
Sergey Gonchenko
Keyword(s):  
Area Preserving Maps ◽  
Homoclinic Tangencies ◽  
Area Preserving

Corrigendum: On dynamics and bifurcations of area-preserving maps with homoclinic tangencies (2015 Nonlinearity 28 3027)

Nonlinearity ◽  
2017 ◽  
Vol 30 (3) ◽  
pp. C2-C2
Author(s):  
Amadeu Delshams ◽  
Marina Gonchenko ◽  
Sergey Gonchenko
Keyword(s):  
Area Preserving Maps ◽  
Homoclinic Tangencies ◽  
Area Preserving

MULTIPLIERS OF HOMOCLINIC TANGENCIES AND A THEOREM OF GONCHENKO AND SHILNIKOV ON AREA PRESERVING MAPS

2005 ◽  
Vol 15 (11) ◽  
pp. 3589-3594 ◽  
Author(s):  
VALENTIN AFRAIMOVICH ◽  
TODD YOUNG
Keyword(s):  
Hausdorff Dimension ◽  
Invariant Set ◽  
Differential Invariants ◽  
Invariant Sets ◽  
Area Preserving Maps ◽  
Homoclinic Tangencies ◽  
Area Preserving

We investigate differential invariants for homoclinic tangencies and discuss the role of these invariants in the Hausdorff dimension of invariant sets associated with the tangency and its unfoldings. Further, we give a streamlined proof of a theorem of Goncheko and Shilnikov on the case of a tangency in an area preserving map. Specifically, the invariants determine whether or not a hyperbolic invariant set is formed near the tangency.

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