Random data Cauchy problem for supercritical Schrödinger equations
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Laurent Thomann (2009)
Annales de l'I.H.P. Analyse non linéaire
Kifer, Yuri (1998)
Documenta Mathematica
Dajani, Karma, Meester, Ronald (2003)
International Journal of Mathematics and Mathematical Sciences
Klemm, A., Pokrovskij, A. (1999)
Journal of Applied Mathematics and Stochastic Analysis
Pierre van Moerbeke (1999/2000)
Séminaire Bourbaki
Omer Angel, Alexander S. Kechris, Russell Lyons (2014)
Journal of the European Mathematical Society
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
Sarah Bailey Frick, Karl Petersen (2008)
Annales de l'I.H.P. Probabilités et statistiques
There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.
Michael Benedicks, Marcelo Viana (2006)
Annales de l'I.H.P. Analyse non linéaire
Katarzyna Horbacz (1998)
Annales Polonici Mathematici
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
Miklós Abért, Nikolay Nikolov (2012)
Journal of the European Mathematical Society
We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the ‘rank vs. Heegaard genus’ conjecture on hyperbolic 3-manifolds is incompatible with the ‘fixed price problem’ in topological dynamics.
Madore, Blair (2004)
The New York Journal of Mathematics [electronic only]
E. M. C. D’Agata, G. F. Webb, J. Pressley (2010)
Mathematical Modelling of Natural Phenomena
Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidly spread in the community. Invasion into the hospital setting with replacement of the hospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with both CA-MRSA and HA-MRSA would have important clinical implications given differences in antimicrobial susceptibility profiles and the potential...
Krystyna Ziemian (1989)
Studia Mathematica
Michael Hitrik, Johannes Sjöstrand (2008)
Annales scientifiques de l'École Normale Supérieure
We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable complex window, provided that the...
Magnus Aspenberg (2009)
Fundamenta Mathematicae
We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
Benjamin Hutz (2010)
Acta Arithmetica
Jung Kyu Canci (2010)
Annales de l’institut Fourier
Let be a number field. Let be a finite set of places of containing all the archimedean ones. Let be the ring of -integers of . In the present paper we consider endomorphisms of of degree , defined over , with good reduction outside . We prove that there exist only finitely many such endomorphisms, up to conjugation by , admitting a periodic point in of order . Also, all but finitely many classes with a periodic point in of order are parametrized by an irreducible curve.
Shi, Ying, Zhang, Da-Jun (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Neumann, Sebastian (2009)
Documenta Mathematica
Adam Kanigowski (2014)
Colloquium Mathematicae
We consider special flows over the rotation on the circle by an irrational α under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the devil's staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that α has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy the weak Ratner property. Moreover, we provide...
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