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....
This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which desc...
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 book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Mo...
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...
The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celes...
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 book collects the notes of the lectures given in the "Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanic...
This book focuses on finding all ordinary differential equations that satisfy a given set of properties. It is dedicated to inverse problems of ordinary differential equations, with the Nambu bracket acting as the central tool to the authors approach. The authors start with a characterization of ordinary differential equations in R DEGREESN which have a given set of M N partial and first integrals, before addressing planar polynomial differential systems with a given set of polynomial partial integrals. They continue solving the 16th Hilbert problem (restricted to algebraic limit cycles)...
This book focuses on finding all ordinary differential equations that satisfy a given set of properties. It is dedicated to inverse problems of ord...
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.
This volume puts together several lectures on the Hamilton Systems and celestial mechanics to form a collection of works on the subject. Their relatio...
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.
Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable pla...
