Chaotic Dynamics in Nonlinear Theory

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The book introduces a groundbreaking approach to demonstrating chaotic dynamics through phase-plane analysis and topological horseshoes. It challenges traditional assumptions by proposing less stringent definitions of horseshoes, allowing for the exploration of chaotic behavior without the need for hyperbolicity. This innovative method is applied to various systems, including a vertically driven planar pendulum and a variable-length pendulum, showcasing the presence of chaos-like dynamics in these contexts.