Surfaces in three-dimensional Lie groups.
Symbolic discrepancy and self-similar dynamics
We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems.
Symbolic dynamics and geodesic flows
Symbolic dynamics and Lyapunov exponents for Lozi maps
Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.
Symbolic dynamics, entropy and complexity of the Feigenbaum map at the accumulation point.
Symbolic dynamics for the Rössler folded towel map
Symbolic dynamics of bimodal maps.
Symbolic extensions for nonuniformly entropy expanding maps
A nonuniformly entropy expanding map is any ¹ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a nonuniformly entropy expanding map T with r > 1 has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].
Symbolic extensions in intermediate smoothness on surfaces
We prove that maps with on a compact surface have symbolic extensions, i.e., topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S. Newhouse and T. Downarowicz in dimension two and improves a previous result of the author [11].
Symbolic extensions of smooth interval maps.
Symmetric CNS trinomials.
Symmetric cocycles and classical exponential sums
Symmetric parareal algorithms for hamiltonian systems
The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators are...
Symmetric three-term recurrence equations and their symplectic structure.
Symmetries and constants of the motion for dynamics in implicit form
Symmetries and integrals of motion in optimal control
Symmetries in connection preserving deformations.
Symmetries of control systems
Symmetries of the control systems of the form , , are studied. Some general results concerning point symmetries are obtained. Examples are provided.
Symmetries of the nonlinear Schrödinger equation
Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum of a Zakharov-Shabat operator is symmetric,i.e. for all , if and only if the sequence of gap lengths, , is symmetric with respect to .
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.