Riemann map and holomorphic dynamics.
Right closing almost conjugacy for G-shifts of finite type
A G-shift of finite type (G-SFT) is a shift of finite type which commutes with the continuous action of a finite group G. For irreducible G-SFTs we classify right closing almost conjugacy, answering a question of Bill Parry.
Rigid reparametrizations and cohomology for horocycle flows.
Rigidité de quelques groupes de germes de difféomorphismes.
Using the description of non solvable dynamics by Nakai, we give in this paper a new proof of the rigidity properties of some sub-groups of Diff(C, O). The Cinfinity case is also considered here.
Rigidité différentiable des groupes fuchsiens
Rigidité du flot géodésique de certaines nilvariétés de rang deux
Rigidity and inflexibility in conformal dynamics.
Rigidity and renormalization in one dimensional dynamical systems.
Rigidity of centralizers of diffeomorphisms
Rigidity of critical circle mappings I
We prove that two critical circle maps with the same rotation number in a special set are conjugate for some provided their successive renormalizations converge together at an exponential rate in the sense. The set has full Lebesgue measure and contains all rotation numbers of bounded type. By contrast, we also give examples of critical circle maps with the same rotation number that are not conjugate for any . The class of rotation numbers for which such examples exist contains...
Rigidity of harmonic measure
Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system...
Rigidity of projective conjugacy for quasiperiodic flows of Koch type
For quasiperiodic flows of Koch type, we exploit an algebraic rigidity of an equivalence relation on flows, called projective conjugacy, to algebraically characterize the deviations from completeness of an absolute invariant of projective conjugacy, called the multiplier group, which describes the generalized symmetries of the flow. We then describe three ways by which two quasiperiodic flows with the same Koch field are projectively conjugate when their multiplier groups are identical. The first...
Rigidity of smooth one-sided Bernoulli endomorphisms.
Rigidity properties of -actions on tori and solenoids.
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
Rigorous numerics for the Cahn-Hilliard equation on the unit square.
Robust controller design for modified projective synchronization of Chen-Lee chaotic systems with nonlinear inputs.
Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach
This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered...
Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model
In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...