Some remarks on the abundance of stable periodic orbits inside homoclinic lobes

DOI10.1016/j.physd.2011.09.007zbMath1244.37039OpenAlexW2087084684MaRDI QIDQ655553

Carles Simó, Arturo Vieiro

Publication date: 4 January 2012

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2011.09.007

zbMATH Keywords

chaosdynamical systemsergodicityreturn mapsstability islands

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10)

Related Items

A review of the ``Third integral ⋮ Stability of the phase motion in race-track microtrons ⋮ Return maps, dynamical consequences and applications ⋮ From the Hénon conservative map to the Chirikov standard map for large parameter values ⋮ Dynamics near the invariant manifolds after a Hamiltonian-Hopf bifurcation

Uses Software

• PARI/GP

Cites Work

• Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
• Periodic orbits and stability islands in chaotic seas created by separatrix crossings in slow-fast systems
• Stability islands in the vicinity of separatrices of near-integrable symplectic maps
• Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance
• Distribution of periodic orbits and the homoclinic tangle
• Dynamical traps
• Stability islands in domains of separatrix crossings in slow-fast Hamiltonian systems
• Separatrix maps in Hamiltonian systems
• Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps
• On the absence of stable periodic orbits in domains of separatrix crossings in nonsymmetric slow-fast Hamiltonian systems
• Towards global models near homoclinic tangencies of dissipative diffeomorphisms
• Geometric and statistical properties induced by separatrix crossings in volume-preserving systems
• Exponentially small splitting of invariant manifolds of parabolic points
• Near threshold anomalous transport in the standard map
• Islands of accelerator modes and homoclinic tangles
• Stable periodic motions in the problem on passage through a separatrix
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