scholarly journals Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

2014 ◽  
Vol 19 (6) ◽  
pp. 663-680 ◽  
Author(s):  
Amadeu Delshams ◽  
Marina Gonchenko ◽  
Pere Gutiérrez
Keyword(s):  
Splitting Of Separatrices ◽  
Exponentially Small

scholarly journals The splitting of separatrices for analytic diffeomorphisms

1990 ◽  
Vol 10 (2) ◽  
pp. 295-318 ◽  
Author(s):  
E. Fontich ◽  
C. Simó
Keyword(s):  
Invariant Manifolds ◽  
Complex Singularities ◽  
Homoclinic Points ◽  
Unperturbed Problem ◽  
Splitting Of Separatrices ◽  
Maximum Separation ◽  
Exponentially Small

AbstractWe study families of diffeomorphisms close to the identity, which tend to it when the parameter goes to zero, and having homoclinic points. We consider the analytical case and we find that the maximum separation between the invariant manifolds, in a given region, is exponentially small with respect to the parameter. The exponent is related to the complex singularities of a flow which is taken as an unperturbed problem. Finally several examples are given.

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