Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. We show that for dynamical systems with an invariant subspace in which there is a quasiperiodic torus, the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. [S0031-9007(96)01861-3]

The phase of a chaotic trajectory in autonomous flows is often ignored because of the wide use of the extremely popular Poincaré surface-of-section technique in the study of chaotic systems. We present evidence that, in general, a chaotic flow is practically composed of a small number of intrinsic modes of proper rotations from which the phase can be computed via the Hilbert transform. The fluctuations of the phase about that of a uniform rotation can be described by fractional Brownian random processes. Implications to nonlinear digital communications are pointed out. [S0031-9007 (97)04534-1] PACS numbers: 05.45. + b, 05.40. + j, 89.70. + cMany physical, chemical, and biological processes in nature are described by a set of coupled first-order autonomous differential equations, or autonomous flows. A widely used technique in the study of these systems is the Poincaré surface-of-section technique [1]. On a Poincaré surface of section, the dynamics can be described by a discrete map whose phase-space dimension is one less than that of the original continuous flow. This sectioning technique thus provides a natural link between continuous flows and discrete maps. With a tremendous facilitation in analysis, numerical computation, and visualization, maps also capture many fundamental dynamical properties of flows. These advantages have made the Pioncaré surface-of-section technique one of the most popular analysis tools in nonlinear dynamics and chaos.Despite its usefulness, the Pioncaré surface-of-section technique has a fundamental drawback: The discrete map produced by it contains no information about the phase or timing of the underlying flow. Consider, for instance, the case of a chaotic attractor. Trajectories on the attractor have the property of recurrence.

Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasiperiodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.

No abstract

Introduction:Aortoesophageal fistula is an uncommon but mortal cause of massive upper gastrointestinal bleeding. The most common causes are thoracic aortic aneurisym, foreign body reaction, malignancy and postoperative complication. It can be seen in different pattern on upper gastrointestinal endoscopy. There are surgical, endoscopic and interventional radiological treatment options, however, definitive treatment is surgical intervention. Diagnosis and treatment desicion should be made quickly because of rapid and mortal course.Case report:In this article, a case of aortoesophageal fistula was presented that resulted in mortality as a result of massive bleeding.