Measurable dynamics of -unimodal maps of the interval
Model reduction methods for chaotic systems
Modeling nonlinear dynamics and chaos: a review.
Modélisation de la transition vers la turbulence
Multibump solutions for Hamiltonian systems with fast and slow forcing
Si dimostra l'esistenza di infinite soluzioni «multi-bump» - e conseguentemente il comportamento caotico - per una classe di sistemi Hamiltoniani del secondo ordine della forma per sufficientemente piccolo. Qui , e sono funzioni strettamente positive e periodiche e è un potenziale superquadratico (ad esempio ).
Multifractal analysis of nearly circular Julia set and thermodynamical formalism
New feedback functions for synchronizing chaotic maps.
Newton, Chebyshev, and Halley Basins of Attraction; A Complete Geometric Approach
Nonlinear control of chaotic systems: a switching manifold approach.
Nonlinear dynamics and chaos in a fractional-order HIV model.
Nonlinear filtering of oscillatory measurements in cardiovascular applications.
Off-center reflections: caustics and chaos.
On a one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
On almost specification and average shadowing properties
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in...
On chaotic dynamics in rational polygonal billiards.
On geometric detection of periodic solutions and chaotic dynamics.
On periodic orbits in discrete-time cascade systems.
On quadratic symplectic mappings.
On small stochastic perturbations of mappings of the unit interval
On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...