Reduction of Hamiltonian Systems, Affine Lie Algebras and Lax Equations.
Reduction of infinite dimensional equations.
Reduction of the singularities of foliations and applications
Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type.
Redundancy relations for fault diagnosis in nonlinear uncertain systems
The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into...
Refined measurable rigidity and flexibility for conformal iterated function systems.
Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Reflexively representable but not Hilbert representable compact flows and semitopological semigroups
We show that for many natural topological groups G (including the group ℤ of integers) there exist compact metric G-spaces (cascades for G = ℤ) which are reflexively representable but not Hilbert representable. This answers a question of T. Downarowicz. The proof is based on a classical example of W. Rudin and its generalizations. A~crucial step in the proof is our recent result which states that every weakly almost periodic function on a compact G-flow X comes from a G-representation of X on reflexive...
Regular AF subalgebras of some crossed products.
Regular and chaotic regimes in scalar field cosmology.
Regular and limit sets for holomorphic correspondences
Holomorphic correspondences are multivalued maps between Riemann surfaces Z and W, where Q̃₋ and Q̃₊ are (single-valued) holomorphic maps from another Riemann surface X onto Z and W respectively. When Z = W one can iterate f forwards, backwards or globally (allowing arbitrarily many changes of direction from forwards to backwards and vice versa). Iterated holomorphic correspondences on the Riemann sphere display many of the features of the dynamics of Kleinian groups and rational maps, of which...
Regular projectively Anosov flows on three-dimensional manifolds
We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of -models. We also apply our method to rigidity problems of some group actions.
Regular projectively Anosov flows with compact leaves
This paper concerns projectively Anosov flows with smooth stable and unstable foliations and on a Seifert manifold . We show that if the foliation or contains a compact leaf, then the flow is decomposed into a finite union of models which are defined on and bounded by compact leaves, and therefore the manifold is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible...
Régularisation d'équations de Stratonovitch à sauts entre variétés
Regularity of solutions of the Hamilton-Jacobi equation
Regularity of conjugacies between critical circle maps: an experimental study.
Regularity of distribution of (nα)-sequences
Regularity of local manifolds in dispersing billiards.
Regularity of measure theoretic entropy for geodesic flows of negative curvature: I.