scholarly journals Topological rigidity of generic unfoldings of tangent to the identity diffeomorphisms

2019 ◽  
Vol 69 (3) ◽  
pp. 993-1046
Author(s):  
Javier Ribón
Keyword(s):  
Tangent To The Identity

Summable formal invariant curves of diffeomorphisms

2011 ◽  
Vol 32 (1) ◽  
pp. 211-221 ◽  
Author(s):  
L. LÓPEZ-HERNANZ
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Infinitesimal Generator ◽  
Invariant Curves ◽  
Tangent To The Identity ◽  
Formal Power

AbstractLet F be a tangent to the identity diffeomorphism in (ℂ2,0) and X its infinitesimal generator. We prove that Camacho and Sad’s formal invariant curves of X give summable formal power series, whose sums correspond to the parabolic curves found by Hakim for F and F−1.

scholarly journals Parabolic curves of diffeomorphisms asymptotic to formal invariant curves

2018 ◽  
Vol 2018 (739) ◽  
pp. 277-296 ◽  
Author(s):  
Lorena López-Hernanz ◽  
Fernando Sanz Sánchez
Keyword(s):  
Fixed Points ◽  
Invariant Curve ◽  
Invariant Curves ◽  
Parabolic Curve ◽  
Tangent To The Identity

AbstractWe prove that ifFis a tangent to the identity diffeomorphism at0\in\mathbb{C}^{2}and Γ is a formal invariant curve ofFwhich is not contained in the set of fixed points then there exists a parabolic curve (attracting or repelling) ofFasymptotic to Γ.

scholarly journals Parabolic curves inℂ3

2003 ◽  
Vol 2003 (5) ◽  
pp. 275-294 ◽  
Author(s):  
Marco Abate ◽  
Francesca Tovena
Keyword(s):  
Tangent To The Identity ◽  
Lower Dimensional

We discuss a family of holomorphic self-maps ofℂ3tangent to the identity at the origin presenting dynamical phenomena not appearing for lower-dimensional maps.

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