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電子ブック
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1. Introduction to the Qualitative Theory of Differential Systems : Planar, Symmetric and Continuous Piecewise Linear Systems
by Jaume Llibre, Antonio E. Teruel
出版情報: Basel : Springer Basel : Imprint: Springer, 2014
シリーズ名: Birkhäuser Advanced Texts Basler Lehrbücher ;
オンライン: http://dx.doi.org/10.1007/978-3-0348-0657-2
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Preface
1 Introduction and statement of the main results
2 Basic elements of the qualitative theory of ODEs
3 Fundamental systems
4 Return maps
5 Phase portraits
Index
Bibliography.
Preface
1 Introduction and statement of the main results
2 Basic elements of the qualitative theory of ODEs
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電子ブック
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2. Central Configurations, Periodic Orbits, and Hamiltonian Systems. 1st ed. 2015
by Jaume Llibre, Richard Moeckel, Carles Simó
出版情報: Basel : Springer Basel : Imprint: Birkhäuser, 2015
シリーズ名: Advanced Courses in Mathematics - CRM Barcelona ;
オンライン: http://dx.doi.org/10.1007/978-3-0348-0933-7
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1 The Averaging Theory for Computing Periodic Orbits
Introduction: the classical theory
Averaging theory for arbitrary order and dimension
Three applications of Theorem
2 Lectures on Central Configurations
The n-body problem
Symmetries and integrals
Central configurations and self-similar solutions
Matrix equations of motion
Homographic motions of central configurations in Rd
Albouy-Chenciner reduction and relative equilibria in Rd
Homographic motions in Rd
Central configurations as critical points
Collinear central configurations
Morse indices of non-collinear central configurations
Morse theory for CC's and SBC's
Dziobek configurations
Convex Dziobek central configurations
Generic finiteness for Dziobek central configurations
Some open problems
3 Dynamical Properties of Hamiltonian Systems
Introduction
Low dimension
Some theoretical results, their implementation and practical tools
Applications to Celestial Mechanics
1 The Averaging Theory for Computing Periodic Orbits
Introduction: the classical theory
Averaging theory for arbitrary order and dimension
3.

電子ブック
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3. Qualitative Theory of Planar Differential Systems
by Freddy Dumortier, Jaume Llibre, Joan C. Artés
出版情報: Berlin, Heidelberg : Springer, 2006
オンライン: http://dx.doi.org/10.1007/978-3-540-32902-2
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電子ブック
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4. Geometric Configurations of Singularities of Planar Polynomial Differential Systems : A Global Classification in the Quadratic Case. 1st ed. 2021
by Joan C. Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe
出版情報: Cham : Springer International Publishing : Imprint: Birkhäuser, 2021
オンライン: https://doi.org/10.1007/978-3-030-50570-7
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Part I
Polynomial differential systems with emphasis on the quadratic ones
1 Introduction
2 Survey of results on quadratic differential systems
3 Singularities of polynomial differential systems
4 Invariants in mathematical classification problems
5 Invariant theory of planar polynomial vector fields
6 Main results on classifications of singularities in QS
7 Classifications of quadratic systems with special singularities
Part II
8 QS with finite singularities of total multiplicity at most one
9 QS with finite singularities of total multiplicity two
10 QS with finite singularities of total multiplicity three
11 QS with finite singularities of total multiplicity four
12 Degenerate quadratic systems
13 Conclusions
Part I
Polynomial differential systems with emphasis on the quadratic ones
1 Introduction