The C 1 generic diffeomorphism has trivial centralizer

5 M ay 2 00 7 The centralizer of a C 1 generic diffeomorphism is trivial

Open Sets of Diffeomorphisms with Trivial Centralizer in the C Topology

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

Handling Generic Intrusion Signatures is not Trivial

This article presents work in progress in the context of misuse scenario detection, where the scenarios are combinations of several actions. An example of a masquerading scenario is: \users manage to usurp the identity of someone, say x, then they copy the le /bin/sh and change its access rights such that later executions of the copy will give the privileges of x 1 ." An intrusion detection sys...

A Generic C 1 Map Has No Absolutely Continuous Invariant Probability Measure

Let M be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension d ≥ 1. Let m be some (smooth) volume probability measure in M. Let C(M,M) be the set of C maps M → M, endowed with the C topology. Given f ∈ C(M,M), we say that μ is an acim for f if μ is an f -invariant probability measure which is absolutely continuous with respect to m. Theorem 1. The set R of C map...

Has a Non - Trivial Invariant Subspace

In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely nonunitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary contractions without a non-trivial algebraic element, or (Case 3) contractions which are not completely non-unitary. We know that every operator of (Case 3) has a non-tr...