## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

We consider the isosceles $3$--body problem
with the third particle having a small mass which eventually tend
to zero. Classical McGehee's blow up is not defined because the
matrix of masses becomes degenerate. Following Elbialy [3]
we perform the blow up using the Euclidean norm in the planar
$3$--body problem. We then complete the phase portrait of the flow
in the collision manifold giving the behavior of some branches of
saddle points missing in [3]. The homothetic orbits within
the fixed energy level then provide the necessary recurrence in
order to build a symbolic dynamics. This is done following ideas
of S. Kaplan [6] for the collinear $3$--body problem.
Here the difficulty is the larger number of critical points.

DCDS

In this paper we analyze the non-integrability of the Wilbeforce
spring-pendulum by means of Morales-Ramis theory in where is enough to prove
that the Galois group of the variational equation is not virtually
abelian. We obtain these non-integrability results due to the
algebrization of the variational equation falls into a Heun
differential equation with four singularities and then we apply
Kovacic's algorithm to determine its non-integrability.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]