Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio
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Publication:2812219
DOI10.1137/15M1032776zbMath1352.37164arXiv1507.07397OpenAlexW2218102858MaRDI QIDQ2812219
Marina Gonchenko, Amadeu Delshams, Pere Gutiérrez
Publication date: 16 June 2016
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.07397
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)
Related Items
On \(1:3\) resonance under reversible perturbations of conservative cubic Hénon maps, Stationary phase methods and the splitting of separatrices, Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies, On the ``hidden harmonics associated to best approximants due to quasi-periodicity in splitting phenomena
Cites Work
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- Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies
- Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
- Splitting of separatrices for the Chirikov standard map
- Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems
- Diophantine approximation
- An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
- Hyperbolic tori and asymptotic surfaces in Hamiltonian systems
- Separatrix splitting for systems with three time scales
- Exponentially small splitting of separatrices under fast quasiperiodic forcing
- Exponentially small splitting of separatrices for perturbed integrable standard-like maps
- Topologically crossing heteroclinic connections to invariant tori.
- Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results
- Exponentially small splitting for whiskered tori in Hamiltonian systems: continuation of transverse homoclinic orbits
- Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds
- Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems
- Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
- Dynamics around simple resonant tori in nearly integrable Hamiltonian systems
- Topological methods in the instability problem of Hamiltonian systems
- The \(k\)-Fibonacci sequence and the Pascal 2-triangle
- A new method for measuring the splitting of invariant manifolds
- A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters
- Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
- Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type
- Renormalization of flows on the multidimensional torus close to aKTfrequency vector
- A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
- A renormalization group for Hamiltonians, with applications to KAM tori
- Biasymptotic solutions of perturbed integrable Hamiltonian systems
- TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
- MEL'NIKOV'S APPROXIMATION DOMINANCE: SOME EXAMPLES
- On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
- Continuous averaging in multi-frequency slow-fast systems
- On a homoclinic splitting problem
- Melnikov method and exponentially small splitting of separatrices
