One dimensional dynamics and factors of finite automata
One sided branching in Anosov foliations.
One-dimensional and two-dimensional dynamics of cubic maps.
One-dimensional chain recurrent sets of flows in the 2-sphere.
One-dimensional motion of balls.
One-Parameter Bifurcation Analysis of Dynamical Systems using Maple
This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.
One-parameter families of brake orbits in dynamical systems
We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of brake orbits...
One-parameter family of cubic Kolmogorov system with an isochronous center.
We show the existence of a one-parameter family of cubic Kolmogorov system with an isochronous center in the realistic quadrant.
One-Parameter Flows with the Pseudo Orbit Tracing Property.
One-sided Lebesgue Bernoulli maps of the sphere of degree and .
On-off intermittency in continuum systems driven by the Chen system
Previous studies on on-off intermittency in continuum systems are generally based on the synchronization of identical chaotic oscillators or in nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five- dimensional continuum systems, respectively, where each system has a two- dimensional subsystem driven by the chaotic Chen system. The phenomenon of intermingled basins is observed below the blowout...
Opening gaps in the spectrum of strictly ergodic Schrödinger operators
We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be canonically labelled by an at most countable set defined purely in terms of the dynamics. Which labels actually appear depends on the choice of the sampling function; the missing labels are said to correspond to collapsed gaps. Here we show that for any collapsed gap,...
Operating with external arguments of Douady and Hubbard.
Operator algebras associated with polymorphisms.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Optimal investment under stochastic volatility and power type utility function
2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.
Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
We consider nearly integrable, non-isochronous, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) -perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time by a variational method which does not require the existence of «transition chains of tori» provided by KAM theory. We also prove that our estimate of the diffusion time is optimal as a consequence of a general stability result proved via classical perturbation...
Optimalité systolique infinitésimale de l’oscillateur harmonique
Nous étudions les aspects infinitésimaux du problème suivant. Soit un hamiltonien de dont la surface d’énergie borde un domaine compact et étoilé de volume identique à celui de la boule unité de . La surface d’énergie contient-elle une orbite périodique du système hamiltoniendont l’action soit au plus ?
Optimality of Ruelle's bound for the domain of meromorphy of generalized zeta functions
Optimisation of time-scheduled regimen for anti-cancer drug infusion
The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...