Abstract
Algebraic structures, connected with the asymptotic expansions of perturbations of smooth dynamical systems, are investigated; first of all, the so-called shuffle multiplication for permutations and for iterated integrals.
Similar content being viewed by others
References
A. A. Agrachev and R. V. Gamkrelidze, “Exponential representation of flows and chronological calculus,” Mat. Sb.,107 (149), No. 4, 467–532 (1978).
R. V. Gamkrelidze, A. A. Agrachev, and S. A. Vakhrameev, “Ordinary differential equations on vector bundles, and chronological calculus,” Itogi Nauki i Tekhniki, Ser. Sovr. Probl. Mat. Noveish. Dostizh.,35, 3–107 (1989).
A. A. Agrachev, R. V. Gamkrelidze, and A. V. Sarychev, “Local invariants of smooth control systems,” Acta Appl. Math.,14, No. 3, 191–237 (1989).
N. Bourbaki, Lie Groups and Lie Algebras, Addison-Wesley, Reading (1975).
P. E. Crouch and F. Lamnabhi-Lagarrigue, “Algebraic and multiple integral identities,” Acta Appl. Math.,15, No. 3, 235–274 (1989).
M. Fliess, “Fonctionnelles causales non linéaires et indéterminées non commutatives,” Bull. Soc. Math. France,109, No. 1, 3–40 (1981).
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 39, pp. 3–40, 1991.
Rights and permissions
About this article
Cite this article
Agrachev, A.A., Gamkrelidze, R.V. Volterra series and permutation groups. J Math Sci 71, 2409–2433 (1994). https://doi.org/10.1007/BF02111557
Issue Date:
DOI: https://doi.org/10.1007/BF02111557