Pugh’s general density theorem

Let M be a compact smooth manifoldMathworldPlanetmath. There is a residual subset of Diff1(M) in which every element f satisfies Per(f)¯=Ω(f). In other words: Generically, the set of periodic points of a 𝒞1 diffeomorphism is dense in its nonwandering set.

Here, Diff1(M) denotes the set of all 𝒞1 difeomorphisms from M to itself, endowed with the (strong) 𝒞1 topology.


Title Pugh’s general density theorem
Canonical name PughsGeneralDensityTheorem
Date of creation 2013-03-22 13:40:42
Last modified on 2013-03-22 13:40:42
Owner Koro (127)
Last modified by Koro (127)
Numerical id 8
Author Koro (127)
Entry type Theorem
Classification msc 37C20
Classification msc 37C25
Synonym general density theorem