Exponentially Small Splitting of Separatrices for Whiskered Tori in Hamiltonian Systems

A. Delshams; P. Gutierrez

doi:10.1007/s10958-005-0224-x

Exponentially Small Splitting of Separatrices for Whiskered Tori in Hamiltonian Systems

Journal of Mathematical Sciences ◽

10.1007/s10958-005-0224-x ◽

2005 ◽

Vol 128 (2) ◽

pp. 2726-2746 ◽

Cited By ~ 7

Author(s):

A. Delshams ◽

P. Gutierrez

Keyword(s):

Hamiltonian Systems ◽

Exponentially Small Splitting ◽

Whiskered Tori ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

A Methodology for Obtaining Asymptotic Estimates for the Exponentially Small Splitting of Separatrices to Whiskered Tori with Quadratic Frequencies

Trends in Mathematics - Extended Abstracts Spring 2014 ◽

10.1007/978-3-319-22129-8_6 ◽

2015 ◽

pp. 31-37

Author(s):

Amadeu Delshams ◽

Marina Gonchenko ◽

Pere Gutiérrez

Keyword(s):

Asymptotic Estimates ◽

Exponentially Small Splitting ◽

Whiskered Tori ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio

SIAM Journal on Applied Dynamical Systems ◽

10.1137/15m1032776 ◽

2016 ◽

Vol 15 (2) ◽

pp. 981-1024 ◽

Cited By ~ 3

Author(s):

Amadeu Delshams ◽

Marina Gonchenko ◽

Pere Gutiérrez

Keyword(s):

Frequency Ratio ◽

Exponentially Small Splitting ◽

Whiskered Tori ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Exponentially Small Splitting of Separatrices Associated to 3D Whiskered Tori with Cubic Frequencies

Communications in Mathematical Physics ◽

10.1007/s00220-020-03832-y ◽

2020 ◽

Vol 378 (3) ◽

pp. 1931-1976

Author(s):

Amadeu Delshams ◽

Marina Gonchenko ◽

Pere Gutiérrez

Keyword(s):

Exponentially Small Splitting ◽

Whiskered Tori ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Exponentially small splitting for whiskered tori in Hamiltonian systems: flow-box coordinates and upper bounds

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2004.11.785 ◽

2004 ◽

Vol 11 (4) ◽

pp. 785-826 ◽

Cited By ~ 12

Author(s):

Amadeu Delshams ◽

◽

Pere Gutiérrez ◽

Tere M. Seara ◽

◽

...

Keyword(s):

Hamiltonian Systems ◽

Upper Bounds ◽

Exponentially Small Splitting ◽

Whiskered Tori ◽

Exponentially Small

Download Full-text

Exponentially small splitting for whiskered tori in Hamiltonian systems: continuation of transverse homoclinic orbits

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2004.11.757 ◽

2004 ◽

Vol 11 (4) ◽

pp. 757-783 ◽

Cited By ~ 9

Author(s):

Amadeu Delshams ◽

◽

Pere Gutiérrez ◽

Keyword(s):

Hamiltonian Systems ◽

Homoclinic Orbits ◽

Exponentially Small Splitting ◽

Whiskered Tori ◽

Exponentially Small

Download Full-text

Exponentially Small Splitting in Hamiltonian Systems

Hamiltonian Mechanics - NATO ASI Series ◽

10.1007/978-1-4899-0964-0_15 ◽

1994 ◽

pp. 181-187

Author(s):

Amadeu Delshams ◽

Tere M. Seara

Keyword(s):

Hamiltonian Systems ◽

Exponentially Small Splitting ◽

Exponentially Small

Download Full-text

Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation

Nonlinearity ◽

10.1088/0951-7715/25/5/1367 ◽

2012 ◽

Vol 25 (5) ◽

pp. 1367-1412 ◽

Cited By ~ 10

Author(s):

Marcel Guardia ◽

Tere M Seara

Keyword(s):

Exponentially Small Splitting ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Exponentially small splitting of separatrices, matching in the complex plane and Borel summation

Nonlinearity ◽

10.1088/0951-7715/6/1/004 ◽

1993 ◽

Vol 6 (1) ◽

pp. 57-70 ◽

Cited By ~ 24

Author(s):

V Hakim ◽

K Mallick

Keyword(s):

Complex Plane ◽

Borel Summation ◽

Exponentially Small Splitting ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Melnikov method and exponentially small splitting of separatrices

Physica D Nonlinear Phenomena ◽

10.1016/s0167-2789(96)00133-9 ◽

1997 ◽

Vol 101 (3-4) ◽

pp. 227-248 ◽

Cited By ~ 30

Author(s):

V.G Gelfreich

Keyword(s):

Melnikov Method ◽

Exponentially Small Splitting ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text

Exponentially small splitting of separatrices in a weakly hyperbolic case

Journal of Differential Equations ◽

10.1016/j.jde.2004.10.017 ◽

2005 ◽

Vol 210 (1) ◽

pp. 106-134 ◽

Cited By ~ 5

Author(s):

Inmaculada Baldomá ◽

Ernest Fontich

Keyword(s):

Hyperbolic Case ◽

Exponentially Small Splitting ◽

Splitting Of Separatrices ◽

Exponentially Small

Download Full-text