It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication, we analyze highly specific enzymatic self-replication mediated through an otherwise neutral recognition region, which leads to frequency-dependent replicati...

We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where F$ is the family subsets natural numbers containing arbitrarily long arithmetic progressions. prove several properties operators, we characterize those which are weakly mixing recurrent, show that there but not mixing.

We prove the spaceability of set hypercyclic vectors for shift-like operators. Shift-like operators appear naturally as composition on Lp(X), when underlying space X is dissipative. In process proving main theorem, we provide, among other results independent interest, a characterization weakly mixing dissipative bounded distortion.