A proof of Bertrand's theorem using the theory of isochronous potentials
, 2021 We give an alternative proof for the celebrated Bertrand's theorem as a corollary of the isochronicity of a certain family of ...
Rojas, David, Ortega, Rafael
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Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial [PDF]
, 1999 In this work we study isochronous centers of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree.
García, I.A. +5 more
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First derivative of the period function with applications [PDF]
, 2004 Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function.
E FREIRE +8 more
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Auditory feedback control in adults who stutter during metronome-paced speech I. Timing Perturbation. [PDF]
J Fluency Disord, 2023 Frankford SA +3 more
europepmc +1 more source
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006 This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide with the entire set of all initial data), from which emerge solutions all of which are completely periodic
openaire +6 more sources
The topology and isochronicity on complex Hamiltonian systems with homogeneous nonlinearities [PDF]
In this paper, we study the Hamiltonian differential systems with homogeneous nonlinearity parts on $\mathbb{C}^2$. Firstly, we present a series of topological properties of polynomial Hamiltonian functions, with a particular focus on the characteristics
Yang, Jiazhong, Dong, Guangfeng
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Unpredictability of the "when" influences prediction error processing of the "what" and "where". [PDF]
PLoS One, 2022 Tsogli V, Jentschke S, Koelsch S.
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Period function and normalizers of vector fields in Rn with n−1 first integrals [PDF]
, 2008 We extend the theory that relates period function, normalizers and first integrals, which has been widely developed in R2, to any dimension. In particular, we show how to find n−1 independent normalizers of vector fields in Rn with n−1 independent first ...
Peralta-Salas, D.
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Anti-Correlated Myelin-Sensitive MRI Levels in Humans Consistent with a Subcortical to Sensorimotor Regulatory Process-Multi-Cohort Multi-Modal Evidence. [PDF]
Brain Sci, 2022 Barnden L +8 more
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Renormalisation group and isochronous oscillations
, 2012 We show how the condition of isochronicity can be studied for two-dimensional systems in the renormalisation group (RG) context. We find a necessary condition for the isochronicity of the Cherkas system and another class of cubic ...
Bhattacharjee, J.K. +3 more
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