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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 …

I found the following * exercise (exercise *9) in page 407 of the book of do Carmo "Differential geometry of curves and surfaces". This problem is a classical theorem which is referenced in the book …

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 $ …

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 …

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 \ …

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?

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 …

A $C^{*}$ algebra $A$ is graded by $\mathbb{Z}_{n}$ iff it can be acted by $\mathbb{Z}_{n}$. So we associate the $C^{*}$ algebra $A\rtimes \mathbb{Z}_{n}$ to a $\mathbb{Z}_{n}$-graded $C^{*}$ alg …

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 …

In the usual singular homology of a topological space $X$, one consider the free abelian group generated by all continuous maps from the standard simplex $\Delta^{n}$ to $X$. Now we can r …

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 …

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 $ …