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We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerica ...
This article shows that portfolio constraints can give rise to rational asset pricing bubbles in equilibrium even if there are unconstrained agents in the economy who can benefit from the induced limited arbitrage opportunities. Furthermore, it is shown th ...
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an impor ...
We present a new formulation for autonomous (i.e. time-independent) Dynamical Systems (DS) to perform discrete robot motions with em non-zero velocity at a given target. The proposed model ensures the convergence of all trajectories to the target, and is i ...
The present work belongs to the vast body of research devoted to behaviors that emerge when homogeneous or heterogeneous agents interact. We adopt a stylized point of view in which the individual agents' activities can be assimilated into nonlinear dynamic ...
By continuously scanning a femtosecond laser beam across a fused silica specimen, we demonstrate the formation of self-organized bubbles buried in the material. Rather than using high intensity pulses and high numerical aperture to induce explosions in the ...
We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...
The stability for all generic equilibria of the Lie-Poisson dynamics of the so(4) rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium ...
This paper provides a robustness analysis of the method we recently developed for rhythmic movement assistance using adaptive oscillators. An adaptive oscillator is a mathematical tool capable of extracting high-level features (i.e. amplitude, frequency, o ...
Motion imitation requires reproduction of a dynamical signature of a movement, i.e. a robot should be able to encode and reproduce a particular path together with a specific velocity and/or an acceleration profile. Furthermore, a human provides only few de ...