M. Herman. Some open problems in dynamical systems. In Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), volume 1998, pages 797-808 (electronic). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Recent Results About Stable Ergodicity - Burns, Pugh, Shub, Wilkinson (2000) (3 citations) (Correct)
....due to Ma n e [Ma n2] There is now a large and important body of work in this area. It is closely related to the results that we discuss, but lies a little outside the scope of this survey; we refer the reader to [AlBonVi] BonD ] BonD Puj] BonVi] Cas] D PujUr] D Ro] Do1] He1] [He2], PujSam] Vi] Our central theme is, to quote [PugSh5] that a little hyperbolicity goes a long way in guaranteeing stably ergodic behavior. By a little hyperbolicity we mean partial hyperbolicity, i.e. b) above. More precisely there is a Tf invariant splitting TM = E u E c E s ....
Herman, M., Some open problems in dynamical systems, Proc. of Int. Congress of Math., Vol. II (Berlin,1998). Doc. Math 1998, Extra Vol.II, 797-808 (electronic).
Poincar'e Rotation Number for Maps of the Real Line.. - Jaroslaw Kwapisz.. (Correct)
....module of the displacement function. This however leads (via flow equivalence) to a well known open question about existence of global analogues of the local KAM type results in dimensions higher than one (the circle case) Appreciation of this deep problem can be developed by reading Herman s [12] and following the references therein. 2 Homeomorphisms (with Plateaus) In this section, we prove Theorems 1 and 3, and we establish continuity of the rotation number as a function of the map. We assume thruought this section that f is non decreasing. Proof of Theorems 1 and 3. If OE changes ....
M. R. Herman. Some open problems in dynamical systems. Doc.Math.J.DMV, Extra Volume ICM 1998, II:797--808, 1998.
Positive Kolmogorov-Sinai entropy for the Standard map - Knill (1999) (1 citation) (Correct)
.... orbits [109] Some research towards avoiding elliptic islands by smooth ergodic perturbations of the Chirikov Standard map has been done [132] It is possible to get positive entropy by a smooth C 1 perturbation of the map [58] Whether this is possible with C 1 perturbations is not known [55]. The question whether a dense set in Diff 1 (M) of measure preserving diffeomorphisms on a manifold M has positive metric entropy has been asked in [59] 3 It has been conjectured that there exists a set of parameters with full density at 1 for which the Chirikov Standard map has no ....
M.R. Herman. Some open problems in dynamical systems. Doc. Math. J. DMV, II:797--808. Extra Volume ICM, 1998.
The Obstruction Criterion For Non Existence - Of Invariant Circles (Correct)
No context found.
M. Herman. Some open problems in dynamical systems. In Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), volume 1998, pages 797-808 (electronic).
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC