Abstract
The aim of this paper is to propose a method to study the complete integrability of gradient systems on a odd dimensional statistical manifold with a potential function. We show that these gradient systems are Hamiltonian and completely integrable.
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References
Amari, S.: Differential-Geometrical Methods in Statistics, 2nd Printing, vol. 28. Springer, Tokyo (2012). https://doi.org/10.1007/978-1-4612-5056-2
Arnol’d, V.I., Givental, A.B., Novikov, S.P.: Symplectic Geometry (Dynamical Systems IV), vol. 4. Springer, Heidelberg (2001). https://doi.org/10.1007/978-3-662-06791-8
Fujiwara, A.: Dynamical systems on statistical models (state of art and perspectives of studies on nonliear integrable systems). RIMS Kkyuroku 822, 32–42 (1993). http://hdl.handle.net/2433/83219
Lesfari, A.: Théorie spectrale et probléme non-linéaires. Surv. Math. Appl. 5, 141–180 (2010). http://www.utgjiu.ro/math/sma
Nakamura, Y.: Completely integrable gradient systems on the manifolds of gaussian and multinomial distributions. Jpn. J. Ind. Appl. Math. 10(2), 179–189 (1993). https://doi.org/10.1007/BF03167571
Ovidiu, C., Constantin, U.: Geometric Modeling in Probability and Statistic, vol. 121. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07779-6
Acknowledgements
I gratefully acknowledge all my discussions with members of ERAG of the University of Maroua. I also would like to thank A. Souleymanou of the Higher National School of Polytechnic Yaounde I for encouragement. Thanks are due to Dr. Kemajou Theophile for fruitful discussions.
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Mama Assandje, P.R., Dongho, J., Bouetou, T.B. (2023). Complete Integrability of Gradient Systems on a Manifold Admitting a Potential in Odd Dimension. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14072. Springer, Cham. https://doi.org/10.1007/978-3-031-38299-4_44
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DOI: https://doi.org/10.1007/978-3-031-38299-4_44
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