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DCDS-S

We study the two-body problem moving under the Fock's potential,
where the global flow is fully described. The analysis is separately
performed for negative, zero, and positive energy levels. Many kinds
of orbits are found, some of them being of positive Lebesgue
measure. We also show some unusual features as the coexistence of
fundamentally different orbits for the same energy level and for the
same angular momentum.

DCDS-B

In this paper we apply the averaging theory to a class of
three-dimensional autonomous quadratic polynomial differential
systems of Lorenz-type, to show the existence of limit cycles
bifurcating from a degenerate zero-Hopf equilibrium.

DCDS

Using collinear reversible configurations and some properties of
symmetry we obtain horseshoe periodic orbits in the general
planar three-body problem with masses $m_1\gg m_2 \geq m_3$, which
usually represents a system formed by a planet and two small
satellites; for instance, the system Saturn-Janus-Epimetheus. For the
numerical analysis we have taken the values $m_2/m_1 = 3.5 \times
10^{-4}$ and $m_3/m_1 = 9.7 \times 10^{-5}$ corresponding to $10^5$
times the mass ratios of Saturn-Janus and Saturn-Epimetheus,

DCDS

The material of this special issue of DCDS-A was originally dedicated in honor of
the 65-th birthday of Prof. Ernesto A. Lacomba. Some of the papers in this issue reflect the joyful spirit surrounding this celebration. Sadly, shortly after the preparation of this volume was completed, Prof. Ernesto A. Lacomba passed away on June 26, 2012. Therefore this special issue is also paying a tribute to his long standing mathematical legacy.

The work of Prof. Lacomba comprised research on geometric theory of ordinary differential equations, dynamical systems, and symplectic geometry, with applications to celestial mechanics, classical mechanics, vortex theory, thermodynamics and electrical circuits. Prof.~Lacomba was the leader of a strong research group working in these areas. In 1991 he started organizing, jointly with some members of his group and with other collaborators, the International Symposium on Hamiltonian Systems and Celestial Mechanics (HAMSYS), which became a great success over the next several years. These symposia brought together top researches from several countries, working in the aforementioned topics, as well as many graduate students who had the opportunity to learn from and connect with the experts in the field, and often get inspiration and motivation to improve and finalize their doctoral theses.

The framework for the celebration of the 65-th birthday of Prof. Lacomba was the VI-th edition of HAMSYS, which was held in México D.F. between November 29 -- December 3, 2010.

This symposium assembled an impressive number of highly respected researches who generated important discussions among the participants, presented new problems, and identified future research directions. The emphasis of the talks was on Hamiltonian dynamics and its relationship to several aspects of mechanics, geometric mechanics, and dynamical systems in general. The papers in this volume are an outgrowth of the themes of the symposium. All papers that were submitted to this special issue underwent a through refereeing process typical to any top mathematical journal. The accepted papers form the present issue of DCDS-A.

The symposium received generous support from CONACYT México and UAM-I. Special thanks are due to Universidad Autónoma Metropolitana for hosting the symposium in the beautiful colonial building

The work of Prof. Lacomba comprised research on geometric theory of ordinary differential equations, dynamical systems, and symplectic geometry, with applications to celestial mechanics, classical mechanics, vortex theory, thermodynamics and electrical circuits. Prof.~Lacomba was the leader of a strong research group working in these areas. In 1991 he started organizing, jointly with some members of his group and with other collaborators, the International Symposium on Hamiltonian Systems and Celestial Mechanics (HAMSYS), which became a great success over the next several years. These symposia brought together top researches from several countries, working in the aforementioned topics, as well as many graduate students who had the opportunity to learn from and connect with the experts in the field, and often get inspiration and motivation to improve and finalize their doctoral theses.

The framework for the celebration of the 65-th birthday of Prof. Lacomba was the VI-th edition of HAMSYS, which was held in México D.F. between November 29 -- December 3, 2010.

This symposium assembled an impressive number of highly respected researches who generated important discussions among the participants, presented new problems, and identified future research directions. The emphasis of the talks was on Hamiltonian dynamics and its relationship to several aspects of mechanics, geometric mechanics, and dynamical systems in general. The papers in this volume are an outgrowth of the themes of the symposium. All papers that were submitted to this special issue underwent a through refereeing process typical to any top mathematical journal. The accepted papers form the present issue of DCDS-A.

The symposium received generous support from CONACYT México and UAM-I. Special thanks are due to Universidad Autónoma Metropolitana for hosting the symposium in the beautiful colonial building

*Casa de la primera imprenta de América*. Last but not least, we thank all participants for contributing to a week-long intense and highly productive mathematical experience.
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