Journal of Fixed Point Theory and Applications最新文献

In Dekimpe and Dugardein (J Fixed Point Theory Appl 17:355–370, 2015), Fel’shtyn and Lee (Topol Appl 181:62–103, 2015), the Nielsen zeta function (N_f(z)) has been shown to be rational if f is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether (N_f(z)) is rational for self-maps on solvmanifolds. In this paper, we prove that (N_f(z)) is rational if f is a self-map of a (compact) solvmanifold of dimension (le 5). In any dimension, we show additionally that (N_f(z)) is rational if f is a self-map of an (mathcal{N}mathcal{R})-solvmanifold or a solvmanifold with fundamental group of the form (mathbb {Z}^nrtimes mathbb {Z}).

We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component.

For each representative (mathfrak {B}) of a bordism class in the free loop space of a manifold, we associate a moduli space of finite length Floer cylinders in the cotangent bundle. The left end of the Floer cylinder is required to be a lift of one of the loops in (mathfrak {B}), and the right end is required to lie on the zero section. Under certain assumptions on the Hamiltonian functions, the length of the Floer cylinder is a smooth proper function, and evaluating the level sets at the right end produces a family of loops cobordant to (mathfrak {B}). The argument produces arbitrarily long Floer cylinders with certain properties. We apply this to prove an existence result for 1-periodic orbits of certain Hamiltonian systems in cotangent bundles, and also to estimate the relative Gromov width of starshaped domains in certain cotangent bundles. The moduli space is similar to moduli spaces considered in Abouzaid (J Symp Geom 10(1):27–79, 2012), Abbondandolo and Figalli (J Differ Equ 234:626–653, 2007) and Abbondandolo and Schwarz (Geom Topol 14:1569–1722, 2010) for Tonelli Hamiltonians. The Hamiltonians we consider are not Tonelli, but rather of “contact-type” in the symplectization end.

We prove that Lyapunov stability problem demonstrates pathologies even on the set-theoretical level. Namely, there exists an analytic one-parameter family of 5-jets of vector fields that crosses the set of stable jets by a countable union of disjoint intervals.

We show a Wolff–Denjoy type theorem in the case of a one-parameter continuous semigroup of nonexpansive mappings in which there is a compact mapping. Using the notion of attractor, we are also able to prove some specific properties directly related to the Karlsson–Nussbaum conjecture.

We use relative symplectic cohomology to detect heavy sets, with the help of index bounded contact forms. This establishes a relation between two notions SH-heaviness and heaviness, which partly answers a conjecture of Dickstein–Ganor–Polterovich–Zapolsky in the symplectically aspherical setting.

We study the set of invariant idempotent probabilities for place-dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Mañé potential and the Aubry set, we provide a complete characterization of the densities of such idempotent probabilities. As an application, we provide an alternative formula for the attractor of a class of fuzzy iterated function systems.