[PDF] Top 20 Computability and dynamical systems: a perspective

... stable systems are not dense ...stable systems are no longer seen as the ade- quate class of “robust ...Guckenheimer and Holmes wrote in their book [GH83, ...unstable systems were regarded as ... See full document

... This procedure is an adaptation (we restrict ourselves to differential equa- tions and not inclusions) and extension (this construction works for unbounded domains) of a technique introduced in [PBV95]. ... See full document

... population and result in significant personal, social and economic ...of, and consequently the most effective interventions for, this condition is an area requiring ...of systems governing ... See full document

... applications and are used to describe a large variety of ...ODE and, in some cases, we can also use some qualitative results to better understand the dynamics of the ...on dynamical systems ... See full document

... distresses and crashes which led to troubled years for the real economy and ...families. Dynamical systems emerged in the mathematical finance literature to help comprehending better the ... See full document

... hyperbolic dynamical systems theory began in the Rus- sian school (especially in Anosov’s work) and was further developed from the 1960s onward by the Smale school, with the purpose of giving a solid ... See full document

... nonlinear dynamical systems possessing saddle-node equilibrium points on it is ...boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the ... See full document

... scientific and technological development and political and economic changes charac- terizing Western capitalist societies have led to not only an increasing appreciation of health as a central ... See full document

... properties and the study of trajectories for which the particle velocity grows ...Hamiltonian systems and known as Fermi acceleration ...continuous and discrete time models see 6, 8– 11 ... See full document

... discrete dynamical system. The mathematical setting for a discrete-time dynamical system is a space X and a map ...system) and the map  defines time evolution - the change of the states over ... See full document

... imitation and emulation among individuals; their joint contribution to the understanding of complex problems and the existence of a common code of communication and of some coordinated procedures to ... See full document

... The constrained optimal control of a linear system with a quadratic perfor- mance index has been of considerable concern and is well covered in many pa- pers (see [6] and [8]). One of the methods to solve ... See full document

... coefficients and, therefore, the computational power of the PGPAC does not rely on its capacity to use the infinite amount of information which can be encoded in a real ...conditions and parameters, are ... See full document

... Elaydi and Sacker [28, 29, 30, ...Sacker and Sell ...results and new developments concerning the periodicity of the system and its stability is ...periodic systems of the main stability ... See full document

... topological and metric characterization of orbits in the coexisting ...stable and unstable periodic orbits reinforce the conclusions obtained with typi- cal chaotic ... See full document

... In this paper mathematical model of a me- chanical system consisting of a plate and either one or two beams is derived. Obtained PDEs are reduced to ODEs, and then studied mainly using the fast Fourier ... See full document

... disaster and hazard management) it has been bundled with data, information, knowledge and information ...Monitoring Systems (EMSs), Environmental Monitoring and Analyzing Systems ... See full document

... study computability and noncomputability in initial-value problems (henceforth abbreviated to IVPs) of ordinary differential equations based on the model of computable ...t and ˙ x denotes the ... See full document

... immune defence [7,45]. Increased male exposure to parasites may be mediated by a variety of mechanisms. In mammals, male- biased parasitism is associated with sexual size dimorphism, with males being the larger ... See full document

... In short, a (mechanical) differential analyzer may be seen as a set of interconnected shafts, each of which representing one of the quantities involved in the computation. At an higher level of abstraction, there are ... See full document