Search results for "dynamical system"
showing 10 items of 523 documents
Gibbs and harmonic measures for foliations with negatively curved leaves
2013
In this thesis we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of F-harmonic measure and prove that there exists a natural bijective correspondence between the two. For projective foliated bundles with sphere-fibers without transverse invariant measure, we show the uniqueness of these measures for any Hölder potential on the basis. In that case we also prove that F-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that their conditional measures on the fibers are limits of weighted averages on the orbits of the holonomy group.
Generalized Fibonacci Dynamical Systems
2009
In this paper we consider generalizations of dynamical systems that are based on the Fibonacci sequence. We first study stability properties of such systems for both the continuous and discrete–time case. Then, by considering the Kronecker operator, a further class of dynamical systems is introduced whose outputs can be used to define possible generalization of the golden section. Appli- cations of such system may range from realization of digital filters, manufacturing of tissue with fractal property, etc. Properties of sequences generated by these systems are partially considered and has to be further addressed.
Diffusive energy growth in classical and quantum driven oscillators
1991
We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the ana…
Asymptotic regime in N random interacting species
2005
The asymptotic regime of a complex ecosystem with \emph{N}random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the i-th density species, the extinction of species and the local field acting on the i-th population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the $i^{th}$ species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.
FOUNDATIONS OF FRACTIONAL DYNAMICS
1995
Time flow in dynamical systems is reconsidered in the ultralong time limit. The ultralong time limit is a limit in which a discretized time flow is iterated infinitely often and the discretization time step is infinite. The new limit is used to study induced flows in ergodic theory, in particular for subsets of measure zero. Induced flows on subsets of measure zero require an infinite renormalization of time in the ultralong time limit. It is found that induced flows are given generically by stable convolution semigroups and not by the conventional translation groups. This could give new insight into the origin of macroscopic irreversibility. Moreover, the induced semigroups are generated …
Random cutout sets with spatially inhomogeneous intensities
2015
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.
On invariant measures of finite affine type tilings
2006
In this paper, we consider tilings of the hyperbolic 2-space, built with a finite number of polygonal tiles, up to affine transformation. To such a tiling T, we associate a space of tilings: the continuous hull Omega(T) on which the affine group acts. This space Omega(T) inherits a solenoid structure whose leaves correspond to the orbits of the affine group. First we prove the finite harmonic measures of this laminated space correspond to finite invariant measures for the affine group action. Then we give a complete combinatorial description of these finite invariant measures. Finally we give examples with an arbitrary number of ergodic invariant probability measures.
On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables
2021
In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.
Some notes on a superlinear second order Hamiltonian system
2016
Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.
Solving stochastic differential equations on Homeo(S1)
2004
Abstract The Brownian motion with respect to the metric H 3/2 on Diff( S 1 ) has been constructed. It is realized on the group of homeomorphisms Homeo( S 1 ). In this work, we shall resolve the stochastic differential equations on Homeo( S 1 ) for a given drift Z .