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

DOI10.1088/0951-7715/6/1/004zbMath0769.34036OpenAlexW2023536788MaRDI QIDQ4034136

Vincent Hakim, Kirone Mallick

Publication date: 16 May 1993

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/6/1/004

zbMATH Keywords

separatrix splittingcapillarity effectsrapidly forced systems

Mathematics Subject Classification ID

Singular perturbations for ordinary differential equations (34E15) Abel, Borel and power series methods (40G10) Dynamical systems and ergodic theory (37-XX)

Related Items

Singular Separatrix Splitting and the Melnikov Method: An Experimental Study, Asymptotics beyond all orders and analytic properties of inverse Laplace transforms of solutions, Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones, High-precision computation: mathematical physics and dynamics, Exponentially small splitting of separatrices for difference equations with small step size, Borel summation and splitting of separatrices for the Hénon map, On the distance between separatrices for the discretized logistic differential equation, Exponentially small splitting of heteroclinc orbits: from the rapidly forced pendulum to discrete solitons, Capturing the cascade: a transseries approach to delayed bifurcations, Geometrical approach to the splitting of separatrix for standard-like mappings, Solitary wave solutions of nonlocal sine-Gordon equations, Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hénon map as an example