“Auxiliary Lesson” שעור עזר) #9) Dec. 20, 2007
Dynamics generated by finitely generated subgroups of conformal germs
- Generic subgroups of
are non-solvable.
- Dynamics generated by several germs. Definition of a pseudogroup. Orbits of points.
- Periodicity of germs (finiteness of order) vs. periodicity of orbits. Cycles and limit cycles of pseudogroups.
- Convergence of elements in pseudogroups. Closure.
- Density of orbits. Linear subgroups. Abundance of limit cycles for generic (nonsolvable) subgroups of
- Topological equivalence of subgroups and pseudogroups. Conjugacy of dense linear subgroups.
- Rigidity of nonsolvable subgroups: topological conjugacy implies holomorphic conjugacy.
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Reading: Section 6 (second part) from the book, printing disabled.
