By C. Alonso-González, F. Cano, R. Rosas (auth.), Santiago Ibáñez, Jesús S. Pérez del Río, Antonio Pumariño, J. Ángel Rodríguez (eds.)
This publication includes papers in response to talks given on the foreign convention Dynamical platforms: a hundred years after Poincaré held on the collage of Oviedo, Gijón in Spain, September 2012. It offers an summary of the state-of-the-art within the research of dynamical platforms.
This publication covers a huge diversity of subject matters, targeting discrete and non-stop dynamical platforms, bifurcation thought, celestial mechanics, hold up distinction and differential equations, Hamiltonian platforms and likewise the vintage demanding situations in planar vector fields. It additionally information fresh advances and new tendencies within the box, together with purposes to a variety of disciplines similar to biology, chemistry, physics and economics.
The reminiscence of Henri Poincaré, who laid the rules of the topic, encouraged this exploration of dynamical structures. In honor of this outstanding mathematician, theoretical physicist, engineer and thinker, the authors have made a distinct attempt to put the reader on the frontiers of present wisdom within the discipline.
Read or Download Progress and Challenges in Dynamical Systems: Proceedings of the International Conference Dynamical Systems: 100 Years after Poincaré, September 2012, Gijón, Spain PDF
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The dynamics of the h´enon map. Ann. Math. (2) 133(1), 73–169 (1991) 7. : Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps. Ergod. Theory Dyn. Syst. 12(1), 13–37 (1992) 8. : Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics, vol. 470. Springer, Berlin (1975) 9. : The ergodic theory of Axiom A flows. Invent. Math. 29(3), 181–202 (1975) 10. : Invariant measures for interval maps with different one-side orders.
Consider the curve x D 1; z D y . The saturated of this curve by the flow of the vector field accumulates at the invariant variety x D 0. ı /= . If D ı= we say that there is no transition; otherwise transits to 0 . The situation is similar if < ı= . By doing the inverse process we have a weights transition through the saddle p in the two possible senses. Now, if we start with the intrinsic weight ˛ of a corner p, by applying this previous rule of weights transition, the value ˛ transits by the flow through connected saddles producing an associated weight at each step.
By H¨older Inequality, the same arguments can be carried out under the assumption that d N n =d is uniformly bounded in Lp . /, for some p < 1, as long as we have n 2 Lq . / for all q > 1. 5 Contracting Lorenz Flow Now we consider a geometric Lorenz vector field X0 where replace the usual expanding condition 3 C 1 > 0 in the Lorenz vector field by the contracting condition 3 C 1 < 0: Statistical Stability in Chaotic Dynamics 21 Fig. U / is a singular-hyperbolic attractor (Rovella attractor). Rovella attractor is not robust.