The nonexistence of expansive homeomorphisms of dendroids
The nonexistence of universal metric flows
We consider dynamical systems of the form where is a compact metric space and is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract -limit sets, answering a question by Will Brian.
The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in .
The number of binary rotation words
We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be Θ(n4). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [Problemy Kibernet. 39 (1982) 67–84], then independently by Mignosi [Theoret. Comput. Sci. 82 (1991) 71–84], and others.
The number of buckled states of circular plates
The number of limit cycles of a quintic Hamiltonian system with perturbation.
The obstacle problem and direct products of unfurled swallowtails
The ODE method for some self-interacting diffusions on ℝd
The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝd. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure μt. These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝd, assuming a confinement potential satisfying some conditions. These hypotheses on the confinement...
The omega limit sets of subsets in a metric space
In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the -limit set of is the limit point of the sequence in and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.
The one-sided ergodic Hilbert transform in Banach spaces
Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform . We prove that weak and strong convergence are equivalent, and in a reflexive space also is equivalent to the convergence. We also show that (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup .
The Painlevé III equation and the Iwasawa decomposition.
The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients.
The period function near a polycycle with two semi-hyperbolic vertices
The period of a whirling pendulum
The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point.
The Periodic Behavior of Morse-Smale Diffeomorphisms.
The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero
The periodic structure of non-singular Morse-Smale flows.
The Perron-Frobenius operator on BV. I.
The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites
It is shown that each expansive group action on a Peano continuum having a free dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, it is shown that each Peano continuum having a free dendrite admits no expansive nilpotent group actions.
The Poincaré-Bendixson theorem and arational foliations on the sphere
Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.