Smale’s spectral decomposition theorem

Let M be a compactPlanetmathPlanetmath differentiable manifold and let f:MM be an Axiom A diffeomorphism. The nonwandering set Ω of f can be partitioned into a finite number of compact topologically transitive blocks, called basic blocks:


Moreover, each basic block is partitioned into a finite number of compact subblocks Λij, j=1,,mi such that f(Λij)=Λi(j+1) for 1j<mi and f(Λimi)=Λi1, and Λij is topologically mixing for fmi.

Title Smale’s spectral decomposition theorem
Canonical name SmalesSpectralDecompositionTheorem
Date of creation 2013-03-22 14:28:08
Last modified on 2013-03-22 14:28:08
Owner Koro (127)
Last modified by Koro (127)
Numerical id 4
Author Koro (127)
Entry type Theorem
Classification msc 37D20
Synonym spectral decomposition theorem
Defines basic block