EUDML

Let $F$ be a foliation of the punctured plane $P$ . Any non-compact leaf of $F$ has two ends, which we call leaf-ends. The set $ℰ$ of leaf-ends which converge to the origin has a natural cyclic order. In the case $ℰ$ is infinite, we show that the cyclicly ordered set $β$ , obtained by identifying neighbors in $ℰ$ and filling in the holes according to the Dedeking process, is equivalent to a circle. We show that the set $P ∐ β$ has a natural topology, and it is homeomorphic to $S^{1} \times [0, \infty)$ with respect to this topology.

Classification of Isolated Hypersurface Singularities by Their Moduli Algebras.

Stephen S.-T. Yau; John N. Mather — 1982

Inventiones mathematicae

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Commutators of diffeomorphisms, III: a group which is not perfect.

A criterion for the non-existence of invariant circles

Stability of $C^{\infty}$ mappings, III. Finitely determined map-germs

Stability of $C^{\infty}$ mappings, IV. Classification of stable germs by $R$ -algebras

Action minimizing invariant measures for positive definite Lagrangian systems.

Commutators of Diffeomorphisms

Integrability in Codimension 1

Commutators of Diffeomorphisms: II.

More Denjoy minimal sets for area preserving diffeomorphisms.

Minimal measures.

A curious remark concerning the geometric transfer map.

Concavity of the Lagrangian for quasi-periodic orbits.

Area preserving twist homeomorphism of the annulus.

Variational construction of connecting orbits

Foliations of surfaces I : an ideal boundary

Classification of Isolated Hypersurface Singularities by Their Moduli Algebras.