Interpolating Hamiltonians for a stochastic-web map with quasicrystalline symmetry

Area of Science:

• Nonlinear dynamics
• Mathematical physics
• Chaos theory

Background:

• Stochastic-web maps exhibit complex behavior.
• Quasicrystalline symmetry influences dynamical systems.
• Hamiltonian approximations are crucial for analyzing such systems.

Purpose of the Study:

• To develop a systematic Hamiltonian approximation scheme for a stochastic-web map.
• To investigate the phase portrait evolution of the map.
• To provide bounds for closed invariant curves.

Main Methods:

• Developing a Hamiltonian approximation scheme.
• Calculating interpolating Hamiltonians up to tenth order.
• Analyzing the control parameter 'a' for map dynamics.

Main Results:

• The developed scheme provides bounds for closed invariant curves.
• Structural evolution of the map's phase portrait is investigated for a <= 0.6.
• Higher-order Hamiltonians offer insights into the map's complex dynamics.

Conclusions:

• The Hamiltonian approximation scheme is effective for analyzing quasicrystalline maps.
• The study reveals key aspects of phase portrait evolution and invariant curve behavior.
• This method advances the understanding of complex dynamical systems.