Theory of Orbits

Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ … J Indeed, several of the problems of modern stellar dy­ namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var­ ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con­ sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con­ tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ … ] Indeed, several of the problems of modern stellar dy­ namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var­ ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con­ sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con­ tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics.

In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature.

This book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.

This book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.

We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity.