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Harmonic maps and the associated harmonic map heat flow, in and of themselves, are among the most widely studied topics in the field of geometric analysis. The discovery of the "bubbling" of sequences of harmonic maps, due to Jonathan Sacks and Karen Uhlenbeck , [ 2 ] has been particularly influential, as their analysis has been adapted to many ...
Here, the domain is 0 ≤ b ≤ 1 and 0 ≤ x ≤ 1 . The sine map ( 4-1 ) exhibits qualitatively identical behavior to the logistic map ( 1-2 ) : like the logistic map, it also becomes chaotic via a period doubling route as the parameter b increases, and moreover, like the logistic map, it also exhibits a window in the chaotic region .
"High school physics textbooks" (PDF). Reports on high school physics. American Institute of Physics; Zitzewitz, Paul W. (2005). Physics: principles and problems. New York: Glencoe/McGraw-Hill. ISBN 978-0078458132
Physics – branch of science that studies matter [9] and its motion through space and time, along with related concepts such as energy and force. [10] Physics is one of the "fundamental sciences" because the other natural sciences (like biology, geology etc.) deal with systems that seem to obey the laws of physics. According to physics, the ...
Hénon attractor for a = 1.4 and b = 0.3 Hénon attractor for a = 1.4 and b = 0.3. In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, [1] is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior.
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
During the first half of the 20th century, cartographers began to think seriously about how the features they drew depended on scale. Eduard Imhof, one of the most accomplished academic and professional cartographers at the time, published a study of city plans on maps at a variety of scales in 1937, itemizing several forms of generalization that occurred, including those later termed ...
A diffeomorphism between two Riemannian manifolds is called a conformal map if the pulled back metric is conformally equivalent to the original one. For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is a conformal map.