books
computability of julia sets
p among all computer generated mathematical images julia sets of rational maps occupy one of the most prominent positions . their beauty and complexity can be fascinating . they also hold a deep mathematical content . p computational hardness of julia sets is the main subject of this book . by definition a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification . there are countless programs to draw julia sets . yet as the authors have discovered it is possible to constructively produce examples of quadratic polynomials whose julia sets are not computable . this result is striking it says that while a dynamical system can be described numerically with an arbitrary precision the picture of the dynamics can not be visualized . p the book summarizes the present knowledge most of it from the authors own work about the computational properties of julia sets in a self contained way . it is accessible to experts and students with interest in theoretical computer science or dynamical systems .
hardcover springer 2008 isbn13 9783540685463 isbn10 3540685464
abridged n isbn 13 9783540685463 number in series 1 number of pages 151 publisher springer verlag release date 62135769600000