Definitions for horseshoe map
horse·shoe map

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1. horseshoe mapnoun

   Any of a class of chaotic maps of the square into itself, used in the study of dynamical systems.

WikipediaRate this definition:0.0 / 0 votes

1. Horseshoe map

   In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe. Most points eventually leave the square under the action of the map. They go to the side caps where they will, under iteration, converge to a fixed point in one of the caps. The points that remain in the square under repeated iteration form a fractal set and are part of the invariant set of the map. The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient.In the horseshoe map, the squeezing and stretching are uniform. They compensate each other so that the area of the square does not change. The folding is done neatly, so that the orbits that remain forever in the square can be simply described. For a horseshoe map: there are an infinite number of periodic orbits; periodic orbits of arbitrarily long period exist; the number of periodic orbits grows exponentially with the period; and close to any point of the fractal invariant set there is a point of a periodic orbit.

WikidataRate this definition:0.0 / 0 votes

1. Horseshoe map

   In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe. Most points eventually leave the square under the action of the map. They go to the side caps where they will, under iteration, converge to a fixed point in one of the caps. The points that remain in the square under repeated iteration form a fractal set and are part of the invariant set of the map. The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient. In the horseshoe map the squeezing and stretching are uniform. They compensate each other so that the area of the square does not change. The folding is done neatly, so that the orbits that remain forever in the square can be simply described. For a horseshoe map: ⁕there are an infinite number of periodic orbits;

How to pronounce horseshoe map?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

   British

   Mia

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   Karen

   Australian

   Hayley

   Australian

   Natasha

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   Veena

   Indian

   Priya

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   Neerja

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   Zira

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   Oliver

   British

   Wendy

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   Tessa

   South African

How to say horseshoe map in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of horseshoe map in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of horseshoe map in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Horseshoe_Map
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Horseshoe_Map
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=horseshoe map