• Media type: E-Article
  • Title: Dynamical properties of maps derived from maps with strong negative Schwarzian derivative
  • Contributor: Boyarsky, Abraham
  • Published: Hindawi Limited, 1984
  • Published in: International Journal of Mathematics and Mathematical Sciences
  • Extent: 803-808
  • Language: English
  • DOI: 10.1155/s016117128400082x
  • ISSN: 0161-1712; 1687-0425
  • Keywords: Mathematics (miscellaneous)
  • Abstract: <jats:p>A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$0$" id="E1"><mml:mn>0</mml:mn></mml:math>as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.</jats:p>
  • Description: <jats:p>A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$0$" id="E1"><mml:mn>0</mml:mn></mml:math>as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.</jats:p>
  • Footnote:
  • Access State: Open Access