We consider a diffeomorphism where is a compact manifold. A topological attractor is a compact subset which is (i) invariant: ; (ii) chain recurrent: for any , any , there exists a finite sequence such that ; and (iii) whose basin, , is a neighborhood of . This last property can be stated as: it [...]
Posts Tagged ‘attractors’
Rafael Potrie: Locally generic Diffeomorphisms With No Attractor
Posted in Dynamics, talks, tagged attractors, generic dynamics, partial hyperbolicity, smooth dynamics on July 5, 2010 | Leave a Comment »
Invisible Attractors
Posted in Dynamics, papers, tagged attractors, Dynamics, smooth ergodic theory on June 22, 2009 | Leave a Comment »
Yu. Ilyashenko and A. Negut have discovered the following dynamical phenomenon. Recall that the statistical attractor is the smallest closed set such that almost every orbit spends almost all its time arbitrarily close to . They say that an open set is -invisible if almost every orbit spends a fraction of its time less than [...]
