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Web Geometry of a System of First-Order Autonomous Ordinary Differential Equations

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Abstract

The goal of this paper is to propose Cartan equivalence problem for a system of n first-order autonomous ordinary differential equations (ODEs) under a Web transformation. In fact, we obtain the necessary and sufficient conditions in the form of differential invariants of this system of n first-order ODEs in the Web geometry.

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References

  1. Cartan É. Les probl`emes d‘équivalence, Oeuvres Complètes, part II, Gauthier-Villars, Paris, 1952, pp. 1311–1334.

  2. Gardner RB. The method of equivalence and its applications. In: CBMS-NSF Regional Conference Series in Applied Mathematics, 58. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 1989.

  3. Gardner RB. Differential geometric method, interfacing control theory, vol. 27. Boston: Progress in Mathematics Birkhauser; 1983. pp. 117–180.

  4. Kamran N, ShadwickWF. Cartan’s method of equivalence and the classication of second-order ordinary differential equations, vol. 68. New York: Contemporary Mathematics; 1987. pp. 125–128.

    Google Scholar 

  5. Kamran N, ShadwickWF. Feedback equivalence of control systems. Syst Control Lett 1987;8:463–465.

    Article  Google Scholar 

  6. Olver PJ. Equivalence, invariants and symmetry. Cambridge: Cambridge University Press; 1995.

    Book  MATH  Google Scholar 

  7. Stormark O. Lie’s structural approach to PDE Systems. Cambridge: Cambridge University Press; 2000.

    Book  MATH  Google Scholar 

  8. Teschl G. Ordinary differential equations and dynamical systems. American Mathematical Society (AMS); 2012.

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Acknowledgments

It is a pleasure to thank the anonymous referees for their constructive suggestions and helpful comments which have materially improved the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak-16, Tehran, IR, Iran

    Mehdi Nadjafikhah

  2. Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol, Iran

    Rohollah Bakhshandeh-Chamazkoti

Authors
  1. Mehdi Nadjafikhah
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  2. Rohollah Bakhshandeh-Chamazkoti
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Correspondence to Rohollah Bakhshandeh-Chamazkoti.

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Nadjafikhah, M., Bakhshandeh-Chamazkoti, R. Web Geometry of a System of First-Order Autonomous Ordinary Differential Equations. J Dyn Control Syst 21, 655–663 (2015). https://doi.org/10.1007/s10883-014-9249-0

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  • DOI: https://doi.org/10.1007/s10883-014-9249-0

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