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I would appreciate if you introduce me a reference (paper or book) who address the concept of hyperbolic dynamics but with emphasis on absence of periodic orbits. a possible tit …

Let $X$ be a compact Hausdorff topological space put $A=C(X)$ the $C^*$ algebra of all complex valued continuous functions. The Gelfand correspondence between the category of compact …

You wrote "I believe that orbits space coming from real-analytic foliations should have a "nicer" structure". I think that this nicer structure arises when we consider a more technical "Leaf space" s …

Let $(M,g)$ be a Riemannian manifold with isometric group $G=Iso(M,G)$. The metric gives an isomorphism between tangent and cotangent bundle of $M$. So $g$ induce a natural symplectic structure on $ …

In the literature, is there a non-commutative analogue of the fact that every Riemannian manifold whose isometry group has sharp dimension must be a constant curvature manifold?

In the literature, are there some research around a directed graph associated to a $C^*$ algebra or a ring $A$ whose vertices are projections or idempotents of $A$ and $e$ is connected to $f$ iff $ef= …

Let $A$ be a Banach or a $C^*$ algebra. We consider the differential equation $$(*)\;\;\;\;Z'=Z^2-Z$$ on $A$. Obviously the singularities of this systems are just the idempotents of the …

One can consider an alternative concept of prime matrix as follows: A matrix $A\in M_n(\mathbb{Z})$ is prime if for any factorization $A=BC$ we have either $Det(B)\in \{-1,1\}$ or $Det(C)\in \{-1,1 …

For a self map $f$ on a topological space $X$ we replace "trace" with "determinant" in the alternative Lefschetz formula $$\Lambda(f)=\sum(-1)^i trace(f^*)|H^i(X,\mathbb{Q})$$ So we have $$\Lam …

In your question you mentioned the word "Fredholm index". So I would like to say that in the circle case there are two different interpretations of Fredholm index of certain lin …

Assume that $M$ is a Riemannian manifold which is equipped with symplectic structure $\omega$. Inspired by the definition of "Scalar curvature", one can define the quantity $tr_{\omega} Ric$ where $ …

Let $N$ be a compact Riemanian manifold and $G$ be its isometry group. Let $M=\chi^{\infty}(N)$ be the space of smooth vector fields on $N$. There is a natural right action of $G$ on $M$ with $X.g=g^* …

In the litterature, in particular in the papers on dynamical investigation of polynomial vector fields on the plane, are there some research devoting to study the Green's function for the PDE which is …

A linear $1$-form on $\mathbb{R}^n$ is a $1$-form $\alpha=\sum_i P_i(x_1,x_2,\ldots,x_n)dx_i$ such that each $P_i$ is in the linear form $P_i=\sum_j a_{ij}x_j$. A linear foliation of $\mathbb{R}^n \ …

There is an alternative proof for FTA using "Fredholm operators on Hilbert spaces": Assume that $P(z)=z^n+a_{n-1}z^{n-1}+\ldots+a_1 z+a_0$ has no root in $\mathbb{C}$. Then for every $\epsilon$ the …