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Hindman and Leader first introduced the notion of semigroup of ultrafilters converging to zero for a dense subsemigroups of $((0,infty),+)$. Using the algebraic structure of the Stone-$breve{C}$ech compactification, Tootkabani and Vahed generalized and extended this notion to an idempotent instead of zero, that is a semigroup of ultrafilters converging to an idempotent $e$ for a dense subsemigroups of a semitopological semigroup $(T, +)$ and they gave the combinatorial proof of central set theorem near $e$. Algebraically one can also define quasi-central sets near $e$ for dense subsemigroups of $(T, +)$. In a dense subsemigroup of $(T,+)$, C-sets near $e$ are the sets, which satisfy the conclusions of the central sets theorem near $e$. S. K. Patra gave dynamical characterizations of these combinatorially rich sets near zero. In this paper we shall prove these dynamical characterizations for these combinatorially rich sets near $e$.
Hindman and Leader first introduced the notion of Central sets near zero for dense subsemigroups of $((0,infty),+)$ and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-$breve{C}$ech compactification
We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local funct
The culmination of the papers (arXiv:0905.0518, arXiv:0910.0909) was a proof of the norm convergence in $L^2(mu)$ of the quadratic nonconventional ergodic averages frac{1}{N}sum_{n=1}^N(f_1circ T_1^{n^2})(f_2circ T_1^{n^2}T_2^n)quadquad f_1,f_2in L^i
We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs $fcolon (X,x_0)to (X,x_0)$, where $X$ is a complex surface having $x_0$ as a normal singularity. We prove that as long as $x_0$ is not a cusp
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $delta$ of the network and the frequency $omega$ of the p