English
Related papers

Related papers: Stability of iterated function systems on the circ…

200 papers

In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…

Optimization and Control · Mathematics 2016-03-23 Aivar Sootla , Alexandre Mauroy

In this paper, we first consider the well-posedness and asymptotic behavior of a one-dimensional piezoelectric beam system with control boundary conditions of fractional derivative type, which represent magnetic effects on the system. By…

Analysis of PDEs · Mathematics 2022-08-23 Yanning An , Wenjun Liu , Aowen Kong

We prove a version of the Poincar\'e-Bendixson theorem for certain classes of curves on the 2-sphere which are not required to be the trajectories of an underlying flow or semiflow on the sphere itself. Using this result we extend the…

Dynamical Systems · Mathematics 2026-01-12 Jairo Bochi , Ian D. Morris

We consider the input/output-stability of linear time-invariant single-input/single-output systems in terms of singularities of the transfer function F(s) in Laplace domain. The approach is based on complex analysis. A fairly general class…

Dynamical Systems · Mathematics 2016-03-04 Ansgar Trächtler

It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…

Dynamical Systems · Mathematics 2014-01-09 Antoine Julien

First approach of invariant densities of a Perron Frobenius operator. Asymptotic behaviours of ODE or PDE, as, are most interesting. The associed infinitesimal iteration is. If is partially linear, a random distribution can be asymptotic…

Dynamical Systems · Mathematics 2011-03-31 Guy Cirier

A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner…

Functional Analysis · Mathematics 2026-04-30 Maria F. Gamal'

The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…

Systems and Control · Electrical Eng. & Systems 2020-01-17 Andrea Cristofaro , Francesco Ferrante

We prove that impulsive systems, which possess an ISS Lyapunov function, are ISS for impulse time sequences, which satisfy the fixed dwell-time condition. If the ISS Lyapunov function is the exponential one, we provide stronger result,…

Optimization and Control · Mathematics 2012-12-24 Sergey Dashkovskiy , Andrii Mironchenko

We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…

Optimization and Control · Mathematics 2026-04-22 Jun Liu

Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy…

Dynamical Systems · Mathematics 2017-03-22 G. F. Helminck , F. Twilt

We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…

Dynamical Systems · Mathematics 2015-12-01 Aliasghar Sarizadeh

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP…

Functional Analysis · Mathematics 2013-06-11 Faik Gürsoy , Vatan Karakaya , B. E. Rhoades

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming…

Differential Geometry · Mathematics 2020-07-28 César Rosales

For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…

Dynamical Systems · Mathematics 2015-05-20 Abed Bounemoura

This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an…

Analysis of PDEs · Mathematics 2026-02-23 Ben Bakary Junior Siriki , Adama Coulibaly

We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…

Dynamical Systems · Mathematics 2015-06-11 Laurent Niederman

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…

Dynamical Systems · Mathematics 2015-05-19 Ian Melbourne , Dalia Terhesiu

Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…

Classical Analysis and ODEs · Mathematics 2009-09-25 O. Makarenkov , R. Ortega

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Dynamical Systems · Mathematics 2007-07-03 Matthew M. Peet , Antonis Papachristodoulou , Sanjay Lall