We prove that the meandering set for $$f_a(z)=e^z+a$$ is homeomorphic to space of irrational numbers whenever a belongs Fatou $$f_a$$ . This extends recent results by Vasiliki Evdoridou and Lasse Rempe. It implies radial Julia has topological dimension zero all attracting parabolic parameters, including $$a\in (-\infty ,-1]$$ Similar are obtained Fatou’s function $$f(z)=z+1+e^{-z}$$

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties the dimension, and compare with topological dimension. The defined satisfies various basic example, subsystem is bounded by that original system topologically conjugated systems have same Also, we discuss relation between entropy.

The space-time dynamics generated by a system of reaction-diffusion equations in Rn on its global attractor are studied in this paper. To describe these dynamics the extended (n + 1)-parameter semigroup generated by the solution operator of the system and the n-parameter group of spatial translations is introduced and their dynamic properties are studied. In particular, several new dynamic char...

We prove a that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls. We also discuss a connection between this uniformity condition and some results on the dynamics of the geodesic flow for such surfaces. Finally, we give a short proof of topological entropy rigidity f...