A system of coupled oscillators with magnetic terms: symmetries and integrals of motion.
A tentative answer to the Castel-San Pietro problem.
A theorem on the structural stability of non-autonomous differential equations
A thermodynamic approach to locally symmetric manifolds of higher rank
A three species ecosystem consisting of a prey, predator and a host commensal to the prey.
A topological characterization of holomorphic parabolic germs in the plane
J.-M. Gambaudo and É. Pécou introduced the "linking property" in the study of the dynamics of germs of planar homeomorphisms in order to provide a new proof of Naishul's theorem. In this paper we prove that the negation of the Gambaudo-Pécou property characterizes the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it turns out to be non-trivial except for countably many conjugacy classes....
A topological invariant for pairs of maps
In this paper we develop the notion of contact orders for pairs of continuous self-maps (f, g) from ℝn, showing that the set Con(f, g) of all possible contact orders between f and g is a topological invariant (we remark that Con(f, id) = Per(f)). As an interesting application of this concept, we give sufficient conditions for the graphs of two continuous self-maps from ℝ intersect each other. We also determine the ordering of the sets Con(f, 0) and Con(f, h), for h ∈ Hom(ℝ) such that f ∘ h = h ∘...
A topological structure of solution sets to evolution systems
A topological version of a theorem of Mather on shadowing in monotone twist maps
A toroidal compactification of the Fermi surface for the discrete Schrödinger operator.
A T-S fuzzy model-based adaptive exponential synchronization method for uncertain delayed chaotic systems: an LMI approach.
A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique.
A Unified Theory of Proportion
A Unified Theory of Proportion
A uniform dichotomy for generic cocycles over a minimal base
We consider continuous -cocycles over a minimal homeomorphism of a compact set of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.
A `user-friendly' approach to the dynamical equations of non-holonomic systems.
A variant of gravitational classification
In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement...
A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
A variational approach to homoclinic orbits in Hamiltonian systems.
A variational construction of chaotic trajectories for a Hamiltonian system on a torus
A geometric criterion for the existence of chaotic trajectories of a Hamiltonian system with two degrees of freedom and the configuration space a torus is given. As an application, positive topological entropy is established for a double pendulum problem.