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Fixed points of discrete nilpotent group actions on $S^{2}$

Suely Druck, Fuquan Fang, Sebastião Firmo (2002)

Annales de l’institut Fourier

We prove that for each integer $k \geq 2$ there is an open neighborhood $𝒱_{k}$ of the identity map of the 2-sphere $S^{2}$ , in $C^{1}$ topology such that: if $G$ is a nilpotent subgroup of ${Diff}^{1} (S^{2})$ with length $k$ of nilpotency, generated by elements in $𝒱_{k}$ , then the natural $G$ -action on $S^{2}$ has nonempty fixed point set. Moreover, the $G$ -action has at least two fixed points if the action has a finite nontrivial orbit.

Fixed points, periodic points, and coin-tossing sequences for mappings defined on two-dimensional cells.

Papini, Duccio, Zanolin, Fabio (2004)

Fixed Point Theory and Applications [electronic only]

Flowability of plane homeomorphisms

Frédéric Le Roux, Anthony G. O’Farrell, Maria Roginskaya, Ian Short (2012)

Annales de l’institut Fourier

We describe necessary and sufficient conditions for a fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.

Flows of flowable Reeb homeomorphisms

Shigenori Matsumoto (2012)

Annales de l’institut Fourier

We consider a fixed point free homeomorphism $h$ of the closed band $B = ℝ \times [0, 1]$ which leaves each leaf of a Reeb foliation on $B$ invariant. Assuming $h$ is the time one of various topological flows, we compare the restriction of the flows on the boundary.

Forcing relations for homoclinic orbits of the Smale horseshoe map.

Collins, Pieter (2005)

Experimental Mathematics

Currently displaying 1 – 5 of 5

Page 1

Displaying 1 – 5 of 5

Fixed points of discrete nilpotent group actions on S 2

Fixed points, periodic points, and coin-tossing sequences for mappings defined on two-dimensional cells.

Flowability of plane homeomorphisms

Flows of flowable Reeb homeomorphisms

Forcing relations for homoclinic orbits of the Smale horseshoe map.

Currently displaying 1 – 5 of 5

Fixed points of discrete nilpotent group actions on $S^{2}$