Theory of Transformation Groups I

Sophus Lie

in Springer Books from Springer

Date: 2015
Edition: 2015
ISBN: 978-3-662-46211-9
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Chapters in this book:

Ch Chapter 1 Three Principles of Thought Governing the Theory of Lie

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Ch Chapter 10 Systems of Partial Differential Equations the General Solution of Which Depends Only Upon a Finite Number of Arbitrary Constants

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Ch Chapter 11 The Defining Equations for the Infinitesimal Transformations of a Group

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Ch Chapter 12 Determination of All Subgroups of an $$r$$ r -term Group

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Ch Chapter 13 Transitivity, Invariants, Primitivity

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Ch Chapter 14 Determination of All Systems of Equations Which Admit a Given $$r$$ r -term Group

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Ch Chapter 15 Invariant Families of Infinitesimal Transformations

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Ch Chapter 16 The Adjoint Group

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Ch Chapter 17 Composition and Isomorphism

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Ch Chapter 18 Finite Groups, the Transformations of Which Form Discrete Continuous Families

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Ch Chapter 19 Theory of the Similarity [Aehnlichkeit] of $$r$$ r -term Groups

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Ch Chapter 2 Local Transformation Equations and Essential Parameters

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Ch Chapter 20 Groups, the Transformations of Which Are Interchangeable with All Transformations of a Given Group

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Ch Chapter 21 The Group of Parameters

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Ch Chapter 22 The Determination of All $$r$$ r -term Groups

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Ch Chapter 23 Invariant Families of Manifolds

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Ch Chapter 24 Systatic and Asystatic Transformation Groups

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Ch Chapter 25 Differential Invariants

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Ch Chapter 26 The General Projective Group

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Ch Chapter 27 Linear Homogeneous Groups

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Ch Chapter 28 Approach [Ansatz] Towards the Determination of All Finite Continuous Groups of $$n$$ n -times Extended Space

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Ch Chapter 29 Characteristic Properties of the Groups Which Are Equivalent to Certain Projective Groups

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Ch Chapter 3 Fundamental Differential Equations for Finite Continuous Transformation Groups

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Ch Chapter 4 One-Term Groups and Ordinary Differential Equations

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Ch Chapter 5 Complete Systems of Partial Differential Equations

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Ch Chapter 6 New Interpretation of the Solutions of a Complete System

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Ch Chapter 7 Determination of All Systems of Equations Which Admit Given Infinitesimal Transformations

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Ch Chapter 8 Complete Systems Which Admit All Transformations of a One-term Group

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Ch Chapter 9 Characteristic Relationships Between the Infinitesimal Transformations of a Group

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DOI: 10.1007/978-3-662-46211-9

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