Numerical Chaos, Symplectic Integrators, and Exponentially Small Splitting Distances

B.M. Herbst; Mark J. Ablowitz

doi:10.1006/jcph.1993.1058

Numerical Chaos, Symplectic Integrators, and Exponentially Small Splitting Distances

Journal of Computational Physics ◽

10.1006/jcph.1993.1058 ◽

1993 ◽

Vol 105 (1) ◽

pp. 122-132 ◽

Cited By ~ 25

Author(s):

B.M. Herbst ◽

Mark J. Ablowitz

Keyword(s):

Symplectic Integrators ◽

Exponentially Small Splitting ◽

Exponentially Small

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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

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Exponentially small splitting of heteroclinc orbits: from the rapidly forced pendulum to discrete solitons

Physics Letters A ◽

10.1016/s0375-9601(00)00247-4 ◽

2000 ◽

Vol 269 (2-3) ◽

pp. 120-129 ◽

Cited By ~ 24

Author(s):

P.G. Kevrekidis ◽

C.K.R.T. Jones ◽

T. Kapitula

Keyword(s):

Exponentially Small Splitting ◽

Forced Pendulum ◽

Discrete Solitons ◽

Exponentially Small

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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

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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

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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

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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

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Exponentially Small Splitting for the Pendulum: A Classical Problem Revisited

Journal of Nonlinear Science ◽

10.1007/s00332-010-9068-8 ◽

2010 ◽

Vol 20 (5) ◽

pp. 595-685 ◽

Cited By ~ 11

Author(s):

Marcel Guardia ◽

Carme Olivé ◽

Tere M. Seara

Keyword(s):

Classical Problem ◽

Exponentially Small Splitting ◽

Exponentially Small

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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

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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

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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

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