A first-order canonical set of generalized Jacobi-type variables for hyperbolic orbital motion.
A fixed point theorem for branched covering maps of the plane
It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| ≤ 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree -2 and X has...
A Foliated Metric Rigidity Theorem for Higher Rank Irreducible Symmetric Spaces.
A functional analysis approach to Arnold diffusion
A functional equation characterizing monomial functions used in permanence theory for ecological differential equations.
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
A gallery of iterated correspondences.
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.
A general class of iterative equations on the unit circle
A class of functional equations with nonlinear iterates is discussed on the unit circle . By lifting maps on and maps on the torus to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
A general synchronization method of chaotic communication systems via Kalman filtering
A generalisation of Mahler measure and its application in algebraic dynamical systems
We prove a generalisation of the entropy formula for certain algebraic -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
A generalised Hopf algebra for solitons.
A generalization for Peakon's solitary wave and Camassa-Holm equation.
A generalization of semiflows on monomials
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.
A generalization of the self-dual induction to every interval exchange transformation
We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic...
A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium
A gentle (without chopping) approach to the full Kostant-Toda lattice.
A geometric analysis of dynamical systems with singular Lagrangians
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.