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Sensitivity problems related to certain bifurcations in non-linear recurrence relations / Gumowski, I. (CERN) ; Mira, C. (CNRS)
This paper is concerned with certain qualitative aspects of the sensitivity problem in relation to small variations of a parameter of a system, the behaviour of which can be described by an autonomous recurrence relation: V$_{n+1}$ = F(V$_{n}, \lambda$) (1) V being a vector, $\lambda$ the parameter. The problem consists in the determination of the bifurcation values $\lambda_{0}$ of $\lambda$, i.e. [...]
1969 - Published in : Automatica 5 (1969) 303-317

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Stochastic solutions in a conservative dynamic system / Gumowski, I ; Mira, C
It is known that solutions of autonomous fourth order conservative dynamic systems, or second order non autonomous dynamic systems, with periodic coefficients can be described by an autonomous second order point mapping (a second order recurrence or surface transformation). The recurrence considered in this paper, which arises in the study of particle dynamics in accelerators and storage rings, is x/sub n+1/=y /sub n/+F(x/sub n/), y/sub n+1/=-x/sub n/+F(x/sub n+1/), F(0)=0 with F (x)= mu x+(1- mu )x/sup alpha /, -1< mu <1, alpha =2 and 3. [...]
1973 - Published in : Zagadnienia Drgan Nieliniowych: 14 (1973) , pp. 417-38
In : 6th International Conference on Nonlinear Oscillations, Poznan, Poland, 29 Aug - 4 Sep 1972, pp.417-38

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Determination of the closed invariant curves of a recurrence or of a nonlinear point transformation near to a linear conservative recurrence / Gumowski, I ; Mira, C
Given a nonlinear recurrence dependent on a parameter mu , which, for mu =0, becomes linear and conservative, the author determines, when mu is small, the closed invariant curves of this recurrence as well as their stability. (3 refs)..
1973 - Published in : C. R. Acad. Sci. Paris, A: 276 (1973) , no. 4, pp. 333-6

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Boundaries of stochasticity domains in Hamiltonian systems / Gumowski, I (CERN) ; Mira, C (Toulouse III U.)
1971 Published version: PDF;
In : 8th International Conference on High-Energy Accelerators, CERN, Geneva, Switzerland, 20 - 24 Sep 1971, pp.374-376

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1	Mira, C.
6	Mira, Christian

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