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Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
Riemannian filling-discs van Kampen diagrams
2015/8/26
The diameter of a disc filling a loop in the universal covering of a Riemannian manifold M may be measured extrinsically using the distance function on the ambient space or intrinsically using the ind...
The Forced van der Pol Equation II: Canards in the Reduced System
van der Pol oscillator hybrid dynamical system
2015/8/25
This is the second in a series of papers about the dynamics of the forced van der Pol oscillator
[J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2(2 003), pp. 1–35].
The fi...
The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
van der Pol oscillator hybrid dynamical system
2015/8/25
The forced van der Pol oscillator has been the focus of scientific scrutiny for almost a century, yet
its global bifurcation structure is still poorly understood. In this paper, we present a hybrid s...
Error term improvements for van der Corput transforms
Asymptotic analysis exponential sum trigonometric sum
2012/5/9
We improve the error term in the van der Corput transform for exponential sums
\sum_{a \le n \le b} g(n) exp(2\pi i f(n)).
For many functions g and f, we can extract the next term in the asymptoti...
Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras
Duistermaat-van der Kallen Theorem Mathieu subspaces
2010/12/14
Let G be a group, R an integral domain, and VG the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero.
Stability of the synchronization manifold in nearest neighbors non identical van der Pol-like oscillators
synchronization manifold der Pol oscillators nearest neighbors
2010/4/1
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit...
Van der Pol-Duffing振子的混沌及控制
混沌 振子 Van der Pol-Duffing
2009/11/2
通过相图、全局分叉图、庞加莱映射图对周期激励Van der Pol-Duffing振子的混沌行为进行了分析，利用两种方法实现了该系统的混沌控制，将该系统的混沌行为有效地控制到稳定的周期轨道．
APPLICATION OF ADOMIAN DECOMPOSITION METHOD TO SOLVING THE DUFFING-VAN DER POL EQUATION
Duffing-van der Pol equation Adomian decomposition method regular perturbation method
2008/11/26
In this paper, the Adomian decomposition method and the regular perturbation
method are used to study the Duffing-van der Pol equation. The two series solutions
obtained by each method are compared.
A Refinement of van der Corput's Inequality
Refinement van der Corput's inequality Harmonic number
2008/7/3
In this note, a refinement of van der Corput's inequality is given.
An Application of Van der Corput's Inequality
Van der Corput's inequality Hardy and Littlewood
2008/7/3
An Application of Van der Corput's Inequality.