Asymptotic behavior of periodic solutions in one-parameter families of Li\'{e}nard equations
, 2019 In this paper, we consider one--parameter ($\lambda>0$) families of Li\'enard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of $\lambda>0$.
Cardin, Pedro Toniol +1 more
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Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction [PDF]
, 2017 In this work we first provide sufficient conditions to assure the persistence of some zeros of functions having the form $$g(z,\varepsilon)=g_0(z)+\sum_{i=1}^k \varepsilon^i g_i(z)+\mathcal{O}(\varepsilon^{k+1}),$$ for $|\varepsilon|\neq0$ sufficiently ...
Cândido, Murilo R. +2 more
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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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Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals [PDF]
, 2017 Agraïments: The first author is partially supported by FEDER-UNAB-10-4E-378 and a CAPES grant 88881.
Llibre, Jaume, Teixeira, Marco Antonio
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Polynomial and linearized normal forms for almost periodic differential systems [PDF]
, 2015 Agraïments: The first author is partially supported by NSFC key program of China (no. 11231001). The MINECO/FEDER grant UNAB13-4E-1604. And the third is supported by NSFC for Young Scientists of China (no.
Li, Weigu, Llibre, Jaume, Wu, Hao
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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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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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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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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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Frequency locking of modulated waves
, 2010 We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type.
A. M. Samoilenko +24 more
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