Stable accessibility for partially hyperbolic diffeomorphisms is central to their ergodic theory, and we establish its \(C^1\)-density among 1. all, 2. volume-preserving, 3. symplectic, 4. contact flows. As applications, obtain in each of these 4 categories \(C^1\)-stable topological transitivity, ergodicity, triviality the centralizer.

We show that if (A, f, B) and (B, g, C) are left (right or two-sided) Segal topological algebras for which g(f(A))⊆ g(B)g(f(A)) (g(f(A))⊆ g(f(A))g(B) g(B)g(f(A))∩ g(f(A))g(B), respectively), then g∘ is also a two-sided, respectively) algebra.

We consider a Hilbert space of entire analytic functions on non-separable space, associated with Fock space. show that under some conditions operators, like the differentiation operators and translation are topologically transitive in this

We prove that non-trivial homoclinic classes of C r-generic flows are topo-logically mixing. This implies that given Λ a non-trivial C 1-robustly transitive set of a vector field X, there is a C 1-perturbation Y of X such that the continuation Λ Y of Λ is a topologically mixing set for Y. In particular, robustly transitive flows become topologically mixing after C 1-perturbations. These results...

This paper concerns a generalization of Moulton planes. We consider these semi-classical projective planes over half-ordered fields and completely determine their Lenz-Barlotti classes in the case of finite planes and of ordered planes. We also obtain a characterization of the Desarguesian planes among the semi-classical planes in terms of linear transitivity. These results are applied to (topo...

Rich-club, assortativity and clustering coefficients are frequently used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study sugg...

A Turing machine is topologically transitive if every partial configuration — that is a state, a head position, plus a finite portion of the tape — can reach any other partial configuration, provided that it is completed into a proper configuration. We characterize topological transitivity and study its computational complexity in the dynamical system models of Turing machines with moving head,...

In 1994 Glasner studied the topological characteristic factor for minimal systems. It is shown that up to canonically defined proximal extensions, a family τd= T × T2 ⋯ Td of canonical PI flows order d − 1. this paper, we generalize Glasner’s work product system finitely many systems and give its relative version. As applications, derive several applications related independence pairs along ari...

In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, shadowing and gluing orbit properties, context C 0 incompressible flows generated by Lipschitz vector fields. We prove that a -generic fixed-point free flow satisfies property, it is transitive has dense set points non-wandering set. particular, reparametrized property. als...