Results 1 to 10 of about 471 (23)

Decay of correlations for slowly mixing flows [PDF]

, 2006
We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyperbolic diffeomorphisms for which Young proved polynomial decay of ...
Melbourne, Ian
core   +3 more sources

Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems [PDF]

, 2005
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result.
Melbourne, Ian, Nicol, Matthew
core   +3 more sources

Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators [PDF]

, 2012
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators.
Giulietti P, Hennion H, Keller G, Lasota A, Liverani C, Oliver Butterley, Tsujii M, Tsujii M, Yosida K   +8 more
core   +2 more sources

Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent [PDF]

, 2018
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow.
Caraballo Garrido, Tomás, Langa Rosado, José Antonio, Obaya García, Rafael, Sanz Gil, Ana María   +3 more
core   +3 more sources

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations [PDF]

, 2011
The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$.
Abraham R., Angenent S. B., Angenent S. B., Angenent S. B., Anosov D. V., Arroyo A., Bendixson I., Bonatti C., Bonatti C., Bonatti C., Brunovský P., Brunovský P., Brunovský P., Brunovský P., Chen X.-Y., Crovisier S., Czaja R., Dancer E. N., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fusco G., Fusco G., Fusco G., Fusco G., Galaktianov V. A., GENEVIÈVE RAUGEL, Ghrist R. W., Guckenheimer J., Hale J. K., Hale J. K., Hardt R., Hayashi S., Henry D., Henry D. B., Hirsch M. W., Hirsch M. W., Hirsch M. W., Hirsch M. W., Jolly M., Joly R., Joly R., Joly R., Mallet-Paret J., Matano H., Matano H., Matano H., Newhouse S. E., Nickel K., Nitecki Z., Palis J., Peixoto M. M., Peixoto M. M., Poláčik P., Poláčik P., Poláčik P., Poláčik P., Prizzi M., Pugh C. C., Pugh C. C., Pugh C. C., Pujals E. R., Robinson C., Robinson J. C., Rocha C., Rocha C., ROMAIN JOLY, Ruelle D., Sandstede B., Smale S., Smale S., Smale S., Smale S., Smillie J., Smith H. L., Smith H. L., Sturm C., Wolfrum M.   +79 more
core   +6 more sources

Superpolynomial and polynomial mixing for semiflows and flows [PDF]

, 2018
We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A self-contained proof is given for semiflows. Results for flows are stated
Melbourne, Ian
core   +2 more sources

Open sets of Axiom A flows with Exponentially Mixing Attractors (with Erratum)

, 2018
For any dimension $d\geq 3$ we construct $C^{1}$-open subsets of the space of $C^{3}$ vector fields such that the flow associated to each vector field is Axiom A and exhibits a non-trivial attractor which mixes exponentially with respect to the unique ...
Araújo, Vítor, Butterley, Oliver, Varandas, Paulo   +2 more
core   +1 more source

Invariants for E_0-semigroups on II_1 factors [PDF]

, 2012
We introduce four new cocycle conjugacy invariants for E_0-semigroups on II_1 factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow.
Margetts, Oliver T., Srinivasan, R.
core   +2 more sources

Rates of mixing for non-Markov infinite measure semiflows [PDF]

, 2018
We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincaré map that is uniformly ...
Bruin, Henk, Melbourne, Ian, Terhesiu, Dalia   +2 more
core   +2 more sources

Weak topologies for Carath\'eodory differential equations. Continuous dependence, exponential Dichotomy and attractors [PDF]

, 2018
We introduce new weak topologies and spaces of Carath\'eodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields.
Longo, Iacopo P., Novo, Sylvia, Obaya, Rafael   +2 more
core   +2 more sources