This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of "chaos" present in it; for that the topological entropy is used....

The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these...

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in...

This book collects the notes of the lectures given in the "Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School)" held at Centre de Recerca Matematica (CRM) from January 27th to 31th, 2014. The notes consist of three series of lectures. One is dedicated to the study of periodic solutions of autonomous differential systems in R DEGREESn via the averaging theory, and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying central configurations. And the last one, given by Carles Simo,...

This volume puts together several lectures on the Hamilton Systems and celestial mechanics to form a collection of works on the subject. Their relationship to several aspects of topology, mechanics and dynamical systems in general are also emphasized.

Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable planar quadratic polynomial differential systems.

The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new...