New results on averaging theory and applications [PDF]
, 2016 Agraïments: The first author is supported by CNPq 248501/2013-5. CAPES grant 88881.030454 /2013-01 from the Program CSF-PVEThe usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to ...
Cândido, Murilo R., Llibre, Jaume
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An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z_2 X Z_2 symmetry
, 2014 We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under $\Z_2\times\Z_2$ symmetry.
Marchesiello, Antonella +1 more
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Formal series and numerical integrators: some history and some new techniques [PDF]
, 2015 This paper provides a brief history of B-series and the associated Butcher group and presents the new theory of word series and extended word series. B-series (Hairer and Wanner 1976) are formal series of functions parameterized by rooted trees.
Murua, Ander, Sanz-Serna, Jesus Maria
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On the averaging principle for one-frequency systems. An application to satellite motions
, 2009 This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been introduced to ...
C. Morosi +8 more
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Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension [PDF]
, 2015 Agraïments: FEDER/UNAB10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2012/18780-0. The third author is partially supported by a FAPESP-BRAZIL grant 2012/23591-1 and 2013/21078-8.The orbits of the reversible differential ...
Llibre, Jaume +2 more
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On the averaging principle for one-frequency systems. Seminorm estimates for the error
, 2008 We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in ...
C. Morosi +9 more
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On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria [PDF]
, 2014 The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria.
Gaitsgory, Vladimir +2 more
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A simple piston problem in one dimension
, 2006 We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior.
Anosov D V +13 more
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Remarks on stability of inverted pendula [PDF]
, 2005 Using linearization principle and tools from chronological calculus one establishes a criteria for stabilization of, usually unstable, equilibrium position of Double Inverted Pendula when subject an arbitrary fast oscillation.
Caiado, M. I., Sarychev, A. V.
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Bifurcations from families of periodic solutions in piecewise differential systems
, 2020 Consider a differential system of the form $$ x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon), $$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0 ...
Llibre, Jaume +2 more
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