The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system.
The effect of radiation on the stochastic web.
The emergence of bull and bear dynamics in a nonlinear model of interacting markets.
The entropy conjecture for diffeomorphisms away from tangencies
We prove that every diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive.
The entropy function on an algebraic structure with infinite partition and -preserving transformation generators.
The entropy of algebraic actions of countable torsion-free abelian groups
This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured. The entropy...
The Equichordal Point Problem.
The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.
The equivalence of controlled lagrangian and controlled hamiltonian systems
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The Ergodic Theory of Axiom A Flows.
The evolution of nonlinear dynamics in political science and public administration: Methods, modeling and momentum.
The existence of an a.c.i.p.m. for an expanding map of the interval; the study of a counterexample
The existence of limit cycle for perturbed bilinear systems
In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...
The explosion of singular cycles
The Exponential Map is Not Recurrent.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The Fatou and Julia sets of multivalued analytical functions.
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).