CHAOS AND COMPLEXITY IN QUADRATIC AREA PRESERVING HÉNON MAP WITH APPLICATIONS OF DLI
By
L. M. Saha1 and Til Prasad Sarma2
1IIIMIT, Department of Mathematics, Shiv Nadar University, Gautam Buddh Nagar, Greater Noida, Dadri, Uttar Pradesh, India-201314
2Department of Education in Science and Mathematics, NCERT, Sri Aurobindo Marg, New Delhi, India -110 016
Email: lmsaha.msf@gmail.com,tpsncert@gmail.com
(Received: May 29, 2025; In format: June 10, 2025; Revised: October 09, 2025; Accepted: October 21, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55213
Abstract
Dynamic studies conducted on regular and chaotic evolution of quadratic area-preserving Hénon map. The model considered a good one for general study of dynamical systems of two degrees of freedom. Evolution comprises with formation of very interesting attractors form by phase plane portraits. Assuming some characteristic values of only parameter α of the map displays remarkable variety of shapes in the phase plane.Amazing regular and chaotic attractors drawn during the process of numerical calculations. For some cases Lyapunov exponents drawn and shown by the sides of chaotic attractors. Applications of Dynamic Lyapunov Indicator (DLI) made here for some regular and chaotic cases. The correlation dimension of some chaotic attractors obtained and presented in a Table form.Topological entropies calculated for some ranges of values of parameter α and very interesting results obtained showing presence of significant complexity in Hénon system.Most results presented through graphics are interesting and significant.
2020 Mathematical Sciences Classification: 34D45, 37H15, 34C23, 65P20
Keywords and Phrases: Chaos, Lyapunov Exponents, Bifurcation, Topological Entropy