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Involutions and Differential Equations

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Differential Equations with Involutions

Part of the book series: Atlantis Briefs in Differential Equations ((ABDE))

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Abstract

Involutions, as we will see, have very special properties. This is due to their double nature, analytic and algebraic. This chapter is therefore divided in two sections that will explore the two kinds of properties, arriving at last to some parallelism between involutions and complex numbers for their capability to decompose certain polynomials (see Remark 1.3.6). In this chapter we recall results from several authors.

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Notes

  1. 1.

    This condition is taken in order to be allowed to divide by 2 in the vector space V.

  2. 2.

    Every differentiable involution is a diffeomorphism.

References

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  4. McShane, N.: On the periodicity of homeomorphisms of the real line. Am. Math. Mon. pp. 562–563 (1961)

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  5. Cabada, A., Tojo, F.A.F.: Comparison results for first order linear operators with reflection and periodic boundary value conditions. Nonlinear Anal. 78, 32–46 (2013)

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  7. Cabada, A., Tojo, F.A.F.: Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions. J. Math. Anal. Appl. 412(1), 529–546 (2014)

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Authors and Affiliations

  1. Departamento de Análise Matemática, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Alberto Cabada & F. Adrián F. Tojo

Authors
  1. Alberto Cabada
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  2. F. Adrián F. Tojo
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Correspondence to Alberto Cabada .

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Cabada, A., Tojo, F.A.F. (2015). Involutions and Differential Equations. In: Differential Equations with Involutions. Atlantis Briefs in Differential Equations. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-121-5_1

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