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Dynamique des Variétés Affines
Author(s) -
Aristide Par Tsemo
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610700001848
Subject(s) - affine transformation , mathematics , endomorphism , pure mathematics , conjecture , differentiable function , manifold (fluid mechanics) , mechanical engineering , engineering
An n ‐affine manifold is a differentiable manifold endowed with an atlas whose transition functions are locally affine transformations of R n . The paper studies affine dynamic, that is, affine endomorphisms of affine manifolds. The main goal is to relate the dynamical viewpoint to the completeness problem. In particular, it is shown that the Markus conjecture is true when dim Aff( M , ▿) > dim M − 2.