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Field name	Details
Dewey Class	515
Title	Averaging Methods in Nonlinear Dynamical Systems ([EBook]) / by Jan A. Sanders, Ferdinand Verhulst.
Author	Sanders, Jan A.
Added Personal Name	Verhulst, Ferdinand , 1939-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1985.
Physical Details	X, 249 pages : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 59
ISBN	9781475745757
Summary Note	In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.:
Contents note	1 Basic Material -- 2 Asymptotics of Slow-time Processes, First Steps -- 3 The Theory of Averaging -- 4 Attraction -- 5 Averaging over Spatial Variables: Systems with Slowly Varying Frequency and Passage through Resonance -- 6 Normal Forms -- 7 Hamiltonian Systems -- 8 Appendices.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-4575-7
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Verhulst, Ferdinand, 1939- . author . Sanders, Jan A. . Verhulst, Ferdinand 1939- . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 515 .

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Averaging Methods in Nonlinear Dynamical Systems

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