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Dynamics through First-Order Differential Equations in the Configuration Space
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 cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
The Book of Deeds of James I of Aragon
The 'Book of Deeds' is the first known autobiography by a Christian king. Its author was James I of Aragon (1213-76), known as 'The Conqueror', one of the great political figures of 13th-century Europe and a successful crusader. In his 'Deeds', James describes the turbulent years of his minority, the thrilling capture of Majorca, the methodical conquest of the kingdom of Valencia, the reconquest of the kingdom of Murcia after Castile had failed to hold it, and many of the important events of his reign. While crusade and conquest of Spanish territory from the Muslims and Christian-Muslim relations on the frontier are central features of the account, the 'Deeds' are also a treasure trove of information on the image, power and purpose of monarchy, loyalty and bad faith in the feudal order, the growth of national sentiment, and medieval military tactics. At the same time, the book presents a unique insight into the mind of a medieval ruler, the supreme example we possess of the fears and ambitions of a man at the very centre of events.
Qualitative Theory of Planar Differential Systems
This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.
Differential Equations with Symbolic Computation
This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Celestial Mechanics
This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari'ssolution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were...
Contradictory Muslims in the Literature of Medieval Iberian Christians
This book argues that literary and historiographical works written by Iberian Christians between the twelfth and sixteenth centuries promoted contradictory representations of Muslims in order to advocate for their colonization through the affirmation of Christian supremacy. Ambivalent depictions of cultural difference are essential for colonizers to promote their own superiority, as explained by postcolonial critics and observed in medieval and early modern texts in Castilian, Catalan, and Portuguese, such as the Cantar de mio Cid, Cantigas de Santa Maria, Llibre dels fets, Estoria de España, Crónica geral de 1344, Tirant lo Blanch, and Os Lusíadas. In all these works, the contradictions of Muslim enemies, allies, and subjects allow Christian leaders to prevail and profit through their opposition and collaboration with them. Such colonial dynamics of simultaneous belligerence and assimilation determined the ways in which Portugal, Spain, and later European powers interacted with non-Christians in Africa, Asia, and even the Americas.
Limit Cycles of Differential Equations
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Rechercha Mathematica Barcelona in 2006. It covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations. Both topics are related to the authors' interests in Hilbert's sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.
Hamiltonian Dynamics and Celestial Mechanics
The symbiotic of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.
Hamiltonian Dynamical Systems
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.
Normal Forms, Bifurcations and Finiteness Problems in Differential Equations
Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
