Displaying similar documents to “Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system.”

A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

Peter Smith (1990)

Revista Matemática de la Universidad Complutense de Madrid

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Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application...

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let R ( λ ) be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that ∫ 1 T | R ( t ) | 2 d t = c T 5 2 + O δ ( T 9 4 + δ ) , where c is a specific nonzero constant and δ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that R ( t ) = O δ ( t 3 4 + δ ) .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the 2 n + 1 -dimensional case. ...