Note on a local invertibility
Note on a Poincaré map
Note on commutable functions.
Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism
We give a negative answer to a question put by Nadkarni: Let S be an ergodic, conservative and nonsingular automorphism on . Consider the associated unitary operators on given by and , where φ is a cocycle of modulus one. Does spectral isomorphism of these two operators imply that φ is a coboundary? To answer it negatively, we give an example which arises from an infinite measure-preserving transformation with countable Lebesgue spectrum.
Notes on some recent methods in bifurcation theory
Notes on symplectic non-squeezing of the KdV flow
We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korteweg-de Vries (KdV) flow on the circle . The nonsqueezing result relies on the aforementioned approximations and the finite-dimensional nonsqueezing theorem of Gromov [14]. Unlike the work of Kuksin [22] which initiated the investigation of non-squeezing results for infinite dimensional Hamiltonian systems, the nonsqueezing argument here does not construct a capacity directly. In this way our...
Nouvelle preuve d’un théorème de Yuan et Hunt
Un théorème de Guo-Cheng Yuan Brian R. Hunt affirme que, pour mesure de probabilité invariante d’un système dynamique hyperbolique , les fonctions lipschitziennes pour lesquelles est minimisante ont un intérieur non vide (en topologie de Lipschitz) si et seulement si est une orbite périodique de . Je donnerai une nouvelle preuve de ce théorème, ou plutôt d’un énoncé essentiellement équivalent. Je discuterai aussi de la stabilité des orbites périodiques minimisantes de grande période.
Numeration systems, substitution dynamical systems and Rauzy fractals.
Numerical Approximations of the Dynamical System Generated by Burgers’ Equation with Neumann–Dirichlet Boundary Conditions
Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...
Numerical bifurcation of separable parameterized equations.
Numerical exploration of Kaldorian interregional macrodynamics: enhanced stability and predominance of period doubling under flexible exchange rates.
Numerical exploration of Kaldorian macrodynamics: Enhanced stability and predominance of period doubling and chaos with flexible exchange rates.
Numerical exploration of Kaldorian macrodynamics: Hopf-Neimark bifurcations and business cycles with fixed exchange rates.
Numerical integration of differential equations in the presence of first integrals: observer method
We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum...
Numerical simulations through first order nonlinear difference equation to study highly ductile symmetric fold (HDSF) dynamics: A conceptual study.
Numerical solution of a stochastic model of a ball-type vibration absorber
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can...
Numerical solutions of a fractional predator-prey system.
Numerical study of invariant sets of a quasiperiodic perturbation of a symplectic map.