A subshift of finite type in the Takens-Bogdanov bifurcation with symmetry.
A sufficient condition for the existence of multiple periodic solutions of differential inclusions
A sufficient condition for -stability of vector fields on open manifolds
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
A survey of Nambu-Poisson geometry.
A survey of random processes with reinforcement.
A survey of results on density modulo of double sequences containing algebraic numbers
In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.
A survey on Nambu-Poisson brackets.
A survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages
The main goal of this paper is the investigation of a relevant property which appears in the various definition of deterministic topological chaos for discrete time dynamical system: transitivity. Starting from the standard Devaney's notion of topological chaos based on regularity, transitivity, and sensitivity to the initial conditions, the critique formulated by Knudsen is taken into account in order to exclude periodic chaos from this definition. Transitivity (or some stronger versions of it)...
A Symbolic Dynamics for Geodesics on Punctured Riemann Surfaces.
A symplectic fixed point theorem for ...Cpn.
A Symplectic Rigidity Theorem.
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