A 3D Smale horseshoe in a hyperchaotic discrete-time system.
A bumpy metric theorem and the Poisson relation for generic strictly convex domains.
A Case of Monotone Ratio Growth for Quadratic-Like Mappings
This is a study of the monotone (in parameter) behavior of the ratios of the consecutive intervals in the nested family of intervals delimited by the itinerary of a critical point. We consider a one-parameter power-law family of mappings of the form . Here we treat the dynamically simplest situation, before the critical point itself becomes strongly attracting; this corresponds to the kneading sequence RRR..., or-in the quadratic family-to the parameters c ∈ [-1,0] in the Mandelbrot set. We allow...
A chaos-based secure cluster protocol for wireless sensor networks
Security mechanisms for wireless sensor networks (WSN) face a great challenge due to the restriction of their small sizes and limited energy. Hence, many protocols for WSN are not designed with the consideration of security. Chaotic cryptosystems have the advantages of high security and little cost of time and space, so this paper proposes a secure cluster routing protocol based on chaotic encryption as well as a conventional symmetric encryption scheme. First, a principal-subordinate chaotic function...
A chaotic function with zero topological entropy having a non-perfect attractor
A characterization of chaotic functions with entropy zero via their maximal scrambled sets
In this note we characterize chaotic functions (in the sense of Li and Yorke) with topological entropy zero in terms of the structure of their maximal scrambled sets. In the interim a description of all maximal scrambled sets of these functions is also found.
A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces
denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle of which is invariant under both the geodesic and the horocycle flows.
A Closing Lemma on the Interval.
A general synchronization method of chaotic communication systems via Kalman filtering
A global perspective for non-conservative dynamics
A modified strong squeezing property and the existence of inertial manifolds of semiflows
A new chaotic attractor from 2D discrete mapping via border-collision period-doubling scenario.
A new curvature invariant and entropy of geodesic flow.
A new model for the transport of particles in a thermostatted system.
A new scenario in dissipative systems: sequential extinction of strange attractors
A note on counting cuspidal excursions.
A note on generic chaos
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
A note on pseudo-Anosov maps with small growth rate.
A note on strange nonchaotic attractors
For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties: 1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e point in is , but for a residual set of points in the omega limit is the...
A note on the asymptotics of perturbed expanding maps.