A generic method for constructing n-fold covers of 3D conservative chaotic systems

Area of Science:

• Dynamical Systems
• Chaos Theory
• Mathematical Physics

Background:

• Conservative chaotic systems are fundamental in understanding complex dynamics.
• Generalized Hamiltonian systems provide a theoretical framework for analyzing such systems.
• Constructing n-fold covers of these systems is crucial for exploring higher-dimensional chaotic behaviors.

Purpose of the Study:

• To propose a generic method for constructing n-fold covers of 3D conservative chaotic systems.
• To investigate the theoretical and numerical properties of these constructed systems.
• To demonstrate the effectiveness of the method using specific examples.

Main Methods:

• Derivation from the theory of generalized Hamiltonian systems.
• Construction of three example systems.
• Theoretical analysis and numerical simulations (Lyapunov exponents).

Main Results:

• Successful construction of various n-fold covers (e.g., 3-fold, 2x3-fold, 2x3x2-fold).
• Verification of conservative and chaotic nature of motion trajectories.
• Identification of the Hamiltonian's crucial role in the emergence of n-fold cover conservative chaos.

Conclusions:

• The proposed generic method is effective for constructing n-fold covers of 3D conservative chaotic systems.
• The Hamiltonian plays a key role in achieving n-fold cover conservative chaos.
• Changing the Hamiltonian, with appropriate skew-symmetric matrices, allows for obtaining n-fold cover conservative chaos.