Symmetry and bifurcation of fixed points of area preserving maps

DOI10.1016/0022-0396(78)90044-XzbMath0399.47049MaRDI QIDQ1254725

Russell Rimmer

Publication date: 1978

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Area Preserving MapsBifurcation of Fixed PointsSymmetric Fixed Points

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Implicit function theorems, Jacobians, transformations with several variables (26B10) General theory for ordinary differential equations (34A99)

Related Items

Periodic orbits for reversible, symplectic mappings, Weakly nonlinear non-symmetric gravity waves on water of finite depth, Linear stability of symplectic maps, Bifurcations of families of 1D-tori in 4D symplectic maps, Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth, Periodic librations and their effect on the quantum energy spectrum, Chaos in a restricted problem of rotation of a rigid body with a fixed point, Lower-dimensional tori in reversible systems, Generic bifurcation from symmetric fixed points of involutory area preserving maps, The reversible umbilic bifurcation, Symmetry and bifurcation of fixed points of area preserving maps, Homoclinic bifurcations for the Hénon map, Bifurcations in two-dimensional reversible maps, Reversible polynomial automorphisms of the plane: the involutory case, Generalized Hénon maps: The cubic diffeomorphisms of the plane

Cites Work

• Local properties of smooth maps equivariant with respect to finite group actions
• Symmetry and bifurcation of fixed points of area preserving maps
• Generic Bifurcation of Periodic Points
• An exact sequence in differential topology
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