The behaviour of standard map's discrete model

• Main Authors: Rosli, Muhammad A'dli, Wan Rozali, Wan Nur Fairuz Alwani
• Format: Conference or Workshop Item
• Language: English
• Published: Department of Computational and Theoretical Sciences, KOS, IIUM 2022
• Subjects: AC Collections. Series. Collected works; QA Mathematics
• Online Access: http://irep.iium.edu.my/103806/1/103806_The%20behaviour%20of%20standard%20map%27s%20discrete%20model.pdf; http://irep.iium.edu.my/103806/; https://www.iium.edu.my/kulliyyah/kos/computational-theoretical-sciences
• Institution: Universiti Islam Antarabangsa Malaysia

Many researchers have done the research about Chrikov-Taylor standard map. However, the studies that they did were in cylinder phase space. Not many people do research of this map in discrete space which we will use this space in our research. Our study focuses on the discrete model to investigate how the discrete points behave. Our objectives of this research are to reduce the 2-dimensional discrete standard map into 1-dimensional map and to investigate the behaviour of the discrete points of the discrete model. We use the Poincaré surface of section to reduce the 2-dimensional of discrete map to 1-dimensional map. The positive X-axis will be our Poincaré surface of section which will be used to investigate in deep of the points on that axis. We classify our map into 2 cases which are case 2 \beta > \alpha and case 2 \beta > \alpha. Finally, we found that the map is interval-exchange transformation.