Systèmes dynamiques topologiques I. Étude des limites de cobords
Systèmes hamiltoniens complètement intégrables et déformations d'algèbres de Lie.
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.
Systèmes hamiltoniens k-symplectiques.
We study some properties of the k-symplectic Hamiltonian systems in analogy with the well-known classical Hamiltonian systems. The integrability of k-symplectic Hamiltonian systems and the relationships with the Nambu's statistical mechanics are given.
Systèmes intégrables à -corps sur la droite
Systems of Proportion in Design and Architecture and their Relationship to Dynamical Systems Theory
Systems of rays in the presence of distribution of hyperplanes
Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical distribution...
Systems of Toda Type, Inverse Spectral Problems, and Representation Theory.
Szegő's first limit theorem in terms of a realization of a continuous-time time-varying systems
It is shown that the limit in an abstract version of Szegő's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.
Szemerédi theorem implies Furnsternberg theorem
Szpilrajn type theorem for concentration dimension
Let X be a locally compact, separable metric space. We prove that , where and stand for the concentration dimension and the topological dimension of X, respectively.