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Let $\mathbb{D}=\{z\in \mathbb{R}^2\mid |z|<1\}$ Is it true to say that every homeomorphism of $\mathbb{D}$ is conjugate to a self homeomrphism of the disk extendable to a homeomorphism of $\bar{\math …

Inspired by these two posts on knots orbits of polynomial vector fields on $\mathbb{R}^3$(A polynomial vector field on $\mathbb{R}^3$ which has a knot periodic orbit) and (Are total curvature and the …

Is there a polynomial vector field $$P(x,y,z)\partial_x+Q(x,y,z)\partial_y+R(x,y,z)\partial_z$$ which has a closed orbit $K$ such that $K$ is a non trivial knot?

I am interested in this question since 1999 when I heared the definition of a knot and I read the definition of unknoting and the total curvature of a knot. To what extent can closed orbi …

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 $M$ be a manifold and $\phi_t$ be a smooth flow associated to a smooth vector field on $M$. Are the following 3 conditions equivalent? 1)For every fixed $t$ the diffeomorphism $\phi …

Let $M$ be a compact Riemannian manifold. The norm of vector fields are computed with respect to the metric. Moreover for every distribution $D$, the orthogonal projection on $D$ is den …

According to existing informative and interesting answers one gets that the local dynamical behavior around fixed points or around periodic orbits may generates some obstructions for being conjuga …

Inspired by this question about conjugation of reql analytic maps to a holomorphic function and with a group action view point we ask the following question. The complex Lie group $H=\math …

By a potential space filling curve we mean a continuous function $f:[0,1]\to [0,1]$ such that there is a continuous surgective function $g:[0,1]\to [0,1]^2$ with $f=\pi_1 \circ g$ where $\pi_1 …

The Shub conjecture on topological entropy $h(f)$ of self map f on manifold M says that the topological entropy is greater (or equal) than (to) the log of maximum absolute values of the eigenv …

Let $(M,g)$ be an analytic Riemannian manifold and $X$ be an analytic vector field on $M$. Can we always have a volume form $\Omega$ such that $\operatorname{Div}_{\Omega} X$ is a harmonic …

Let $G$ be a compact topological group with normalized Haar measure $\mu$. An element $g\in G$ is an ergodic element if the mapping $L_g:G \to G $ with $x\mapsto gx$ is an ergodic map. The se …

Let $G$ be a Lie group whose Lie algebra is $\mathfrak{g}$ with exponential map $\exp:\mathfrak{g}\to G$. For what kind of Lie group $G$ the standard process of definition of rotation number …

Is the Poincare-Birkhoff theorem valid if we change the volume form of the annulus region? Note: A possible approach could be the following: Is it true to say that the answer is affirmative beca …