An analytical approach to determine critical parameter values of homoclinic bifurcations in three-dimensional systems is reported. The homoclinic orbit is supposed to be a limit of a unique periodic orbit. Hence, the multiple scales perturbation method is performed to construct an approximation of the periodic solution and its frequency. Then, two simple criteria are used. The first criterion i...

We show the existence of a local solution to a Hamilton–Jacobi–Bellman (HJB) PDE around a critical point where the corresponding Hamiltonian ODE is not hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of the center manifold theo...

We study the action of pseudo-Anosov homeomorphisms f : R → R on the character varieties of SL(2,C) -representations of the fundamental groups π1(R) of closed orientable hyperbolic surfaces R . We prove that the representation π1(R) →֒ SL(2,C) corresponding to the holonomy representation of the hyperbolic structure on the mapping torus of f is a hyperbolic fixed point for the action of f on the ...

Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic perturbations, together with their infinit...

In this paper, we study some group-theoretic constructions associated to arithmetic fundamental groups of hyperbolic curves over finite fields. One of the main results of this paper asserts that any Frobeniuspreserving isomorphism between the geometrically pro-l fundamental groups of hyperbolic curves with one given point removed induces an isomorphism between the geometrically pro-l fundamenta...

today, along with enhancement of social well-being andeconomic development, demand for transportation is growing increasingly.many countries are seeking for providing transportation servicesat a reasonable price. therefore, optimization of carrying goods on nationalor international roads is highly important in terms of costs andtransportation indicator, so that the goods are shipped at minimumc...

There are several ways to generalise the hyperbolic plane and its isometry group to objects in higher dimensions. Perhaps the most familiar is (real) hyperbolic three space, popularised by the work of Thurston [14]. The Poincaré disc and half plane models of the hyperbolic plane naturally come with a complex structure and it is natural to generalise them to complex hyperbolic space in higher co...

We study the class of entire transcendental maps of finite order with one critical point and one asymptotic value, which has exactly one finite pre-image, and having a persistent Siegel disc. After normalisation this is a one parameter family fa with a ∈ C ∗ which includes the semi-standard map λzez at a = 1, approaches the exponential map when a → 0 and a quadratic polynomial when a → ∞. We in...