On the Fixed Point Index of Iterates of Planar Homeomorphisms

DOI10.2307/2047977zbMath0686.58028OpenAlexW4235145691MaRDI QIDQ4204847

Morton B. Brown

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2047977

zbMATH Keywords

fixed point indexorientation preserving homeomorphism

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items

Fixed point indices of iterates of a low-dimensional diffeomorphism at a fixed point which is an isolated invariant set ⋮ Fixed point theorem for non-self maps of regions in the plane ⋮ Fixed points of planar homeomorphisms of the form identity + contraction ⋮ Periodic points of the planar area preserving Poincaré map inside isolating segment ⋮ A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms ⋮ Lefschetz index for orientation reversing planar homeomorphisms ⋮ Periodic points for area-preserving birational maps of surfaces ⋮ Dynamique des homéomorphismes du plan au voisinage d'un point fixe ⋮ Dold sequences, periodic points, and dynamics ⋮ Fixed point indices of planar continuous maps

Cites Work

• L'espace des homéomorphismes du plan qui admettent un seul point fixe d'indice donné est connexe par arcs
• A remark on the Lefschetz fixed point formula for differentiable maps
• Proof of the Poincaré-Birkhoff fixed point theorem
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