In systems exhibiting transient chaos in coexistence with periodic attractors, the inclusion of weak noise might give rise to noise-induced chaotic attractors. When the noise amplitude exceeds a critical value, an extended attractor appears along the fractal unstable manifold of the underlying nonattracting chaotic set. A further increase of noise leads to a fuzzy nonfractal pattern. By means o...

The paper contains a rigorous proof of existence symbolic dynamics chaos in the generalized H\'enon map's 4th iterate $H^4$, which was conjectured \textit{A 3D Smale Horseshoe Hyperchaotic Discrete-Time System} Li and Yang, 2007. We prove also uniform hyperbolicity invariant set with dynamics. proofs are computer-assisted use C++ library \textit{CAPD} for interval arithmetic, differentiation in...

Let T : I ?! I be a Lasota-Yorke map on the interval I, let Y be a non trivial sub-interval of I and g 0 : I ?! R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to non absorption in Y. These conditions imply also...

This paper presents a new hyperchaotic system with three positive Lyapunov exponents (called Tri-Chaos). Via linear coupling, Mathieu, and van der Pol systems are coupled with each other and then become a new four order system—Mathieu–van der Pol autonomous system. As we know, two positive Lyapunov exponents confirm hyperchaotic nature of its dynamics and it means that the system can present mo...

We prove stability of the isolated eigenvalues of transfer operators satisfying a Lasota-Yorke type inequality under a broad class of random and nonrandom perturbations including Ulam-type discretizations. The results are formulated in an abstract framework.

We study general dynamical and topological behaviors of minimal sets in skewproduct circle flows in both continuous and discrete settings, with particular attentions paying to almost periodically forced circle flows. When a circle flow is either discrete in time and unforced (i.e., a circle map) or continuous in time but periodically forced, behaviors of minimal sets are completely characterize...