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Consider a surface $S$ and a vector field on the surface which has a closed orbit. The vector field on both sides of the closed orbit spirals towards it, which gives us that the linearized Poincare ...

Let $b:\mathbb R_+ \times \mathbb R^d \to \mathbb R^d$ be measurable such that for all $n \in \mathbb N$ we have $$ \sup_{t \ge 0} |b(t, 0)| + \sup_{t \ge 0} \sup_{x \in \mathbb R^d} |\nabla^n_x b (t, ...

In working with binary collisions in the Hamiltonian formulation of the Newtonian $n$-body problem, two common regularization techniques that deal with binary collisions are the Levi-Civita technique, ...

In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The ...

There is a famous result shows that for every continuous function $f:{\mathbb R}\rightarrow {\mathbb R}$, the first order autonomous system $$ \left\{ \begin{array}{l} \dot{x}=f(x), \\ x(t_0)=x_0, \...