Search

This article discusses vector fields in $\mathbb R^n$, $n \geq 3$, that can be written as the sum of a radial repelling vector field and an attracting nonlinear homogeneous vector field of odd degree. The nontrivial dynamics for such vector fields is restricted to an invariant topological sphere. A necessary and sufficient condition for this invariant topological sphere to be the unit sphere centered at the origin of coordinates is given. Examples exhibiting distinct dynamics on these invariant spheres are presented.

We study the number of limit cycles bifurcating from the origin of a Hamiltonian system of degree 4. We prove, using the averaging theory of order 7, that there are quartic polynomial systems close these Hamiltonian systems having 3 limit cycles.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

On the invariant sphere theorem with emphasis in the round sphere $\mathbb S^n$

Limit Cycles of a Perturbation of a Polynomial Hamiltonian Systems of Degree 4 Symmetric with Respect to the Origin

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

On the invariant sphere theorem with emphasis in the round sphere $\mathbb S^n$

Limit Cycles of a Perturbation of a Polynomial Hamiltonian Systems of Degree 4 Symmetric with Respect to the Origin