An automatized method to search for complex symbolic dynamics is proposed. The method can be used to show that a given dynamical system is chaotic in the topological sense. Application of this method in the analysis of a third-order memristor circuit is presented. Several examples of symbolic dynamics are constructed. Positive lower bounds for the topological entropy of an associated return map...

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested i...

The aim of this paper is to introduce a method for computing rigorous lower bounds for topological entropy. The topological entropy of a dynamical system measures the number of trajectories that separate in finite time and quantifies the complexity of the system. Our method relies on extending existing computational Conley index techniques for constructing semi-conjugate symbolic dynamical syst...

Each topological group G admits a unique universal minimal dynamical system (M(G), G). For a locally compact non-compact group this is a nonmetrizable system with a very rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space ...

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.