Statistics of Poincaré recurrences for a class of smooth circle maps
نویسندگان
چکیده
Statistics of Poincaré recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the statistics of the return times.
منابع مشابه
Examples of non-rigidity for circle homeomorphisms with breaks
We give examples of analytic circle maps with singularities of break type with the same rotation number and the same size of the break for which no conjugacy is Lipschitz continuous. In the second part of the paper, we discuss a class of rotation numbers for which a conjugacy is C1-smooth, although the numbers can be strongly non-Diophantine (Liouville). For the rotation numbers in this class, ...
متن کاملAsymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
During the last two decades the local structure of the phase space of chaotic Hamiltonian systems and areapreserving maps has been studied in great detail [1–5]. These studies allow one to understand the universal scaling properties in the vicinity of critical invariant curves where coexistence of chaos and integrability exists on smaller and smaller scales in the phase space. The most studied ...
متن کاملUnimodularity of Poincaré Polynomials of Lie Algebras for Semisimple Singularities
We single out a large class of semisimple singularities with the property that all roots of the Poincaré polynomial of the Lie algebra of derivations of the corresponding suitably (not necessarily quasihomogeneously) graded moduli algebra lie on the unit circle; for a still larger class there might occur exactly four roots outside the unit circle. This is a corrected version of a theorem by Ela...
متن کاملAsymptotic Likelihood of Chaos for Smooth Families of Circle Maps
Abstract. We consider a smooth two-parameter family fa,L : θ 7→ θ+a+LΦ(θ) of circle maps with a finite number of critical points. For sufficiently large L we construct a set A (∞) L of a-values of positive Lebesgue measure for which the corresponding fa,L exhibits an exponential growth of derivatives along the orbits of the critical points. Our construction considerably improves the previous on...
متن کاملRecurrences in multiple-particle Billiard systems
We investigate recurrence statistics of two-particle circular billiards. Dynamics of this billiard is generated by free-motion of two particles (with non-zero radius) inside a closed surface with piecewise smooth circular boundary in 2−D Euclidean space. Particles collide elastically against the boundary and each other, with angle of incidence equal to angle of reflection. We are interested in ...
متن کامل