On the symmetry lines of the standard mapping

DOI10.1016/0167-2789(87)90236-3zbMath0612.58023OpenAlexW2036503556MaRDI QIDQ1088233

E. Piña, Lidia Jiménez-Lara

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90236-3

zbMATH Keywords

Poincaré sectiondynamics of non-integrable systemsTaylor and Chirikov standard mapping

Mathematics Subject Classification ID

Topological dynamics (37B99) Iteration of real functions in one variable (26A18)

Related Items (17)

KAM theorems for the product of two involutions of different types ⋮ The iteration-approximation decoupling in the reversible KAM theory ⋮ Reversing \(k\)-symmetries in dynamical systems ⋮ Bifurcations of families of 1D-tori in 4D symplectic maps ⋮ Orbits of charged particles with an azimuthal initial velocity in a dipole magnetic field ⋮ The planar three-body problem, symmetries and periodic orbits ⋮ Periodic orbits for anisotropic perturbations of the Kepler problem ⋮ Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors ⋮ Lower-dimensional tori in reversible systems ⋮ Periodic orbits in \(k\)-symmetric dynamical systems ⋮ Bifurcation of the period-4 orbits in the standard map ⋮ Reversible maps and their symmetry lines ⋮ A new method to compute periodic orbits in general symplectic maps ⋮ Conjugacy classes and chiral doublets in the Hénon Hamiltonian repeller ⋮ Hamiltonian mappings and circle packing phase spaces: numerical investigations ⋮ Symmetry structure of accelerator modes in the standard map ⋮ Computational Study of the Dynamics of an Asymmetric Wedge Billiard

Cites Work

• On universality for area-preserving maps of the plane
• Universal behaviour in families of area-preserving maps
• A renormalization approach to invariant circles in area-preserving maps
• Critical Behavior of a KAM surface. I: Empirical results
• On the stability of periodic orbits of two-dimensional mappings
• A mathematical critique of some physical theories
• Two-Dimensional Measure-Preserving Mappings
• The Lattice Point Covering Theorem for Rectangles
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