In this paper, we use Lyapunov exponents to analyze how the dynamical properties of H\'enon map change as a function coefficients linear filter inserted in its feedback loop. We show that generated orbits can be chaotic or not, depending on coefficients. The dynamics system presents complex behavior, including cascades bifurcations, coexistence attractors, crises, and "shrimps". obtained result...

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

We consider an action of the automorphism group Aut(F n ) free F rank on filtered vector space A d (n) Jacobi diagrams degree oriented arcs. This induces associated graded (n), which is identified with B open diagrams, general linear GL(n,?) and Lie algebra IA-automorphism its lower central series. use these actions to study )-module structure (n). In particular, we case where d=2 in detail giv...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings R[[x]], where R is between Z an...