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.
A version of non-Hamiltonian Liouville equation
In this paper we give a version of the theorem on local integral invariants of systems of ordinary differential equations. We give, as an immediate conclusion of this theorem, a condition which guarantees existence of an invariant measure of local dynamical systems. Results of this type lead to the Liouville equation and have been frequently proved under various assumptions. Our method of the proof is simpler and more direct.