Journal ArticleDOI
Renormalization and Periodic Orbits¶for Hamiltonian Flows
Juan J. Abad,Hans Koch +1 more
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In this article, a renormalization group transformation for analytic Hamiltonians in two or more dimensions is proposed to construct invariant tori, as well as sequences of periodic orbits with rotation vectors approaching that of the invariant Torus.Abstract:
We consider a renormalization group transformation \(\) for analytic Hamiltonians in two or more dimensions, and use this transformation to construct invariant tori, as well as sequences of periodic orbits with rotation vectors approaching that of the invariant torus. The construction of periodic and quasiperiodic orbits is limited to near-integrable Hamiltonians. But as a first step toward a non-perturbative analysis, we extend the domain of \(\) to include any Hamiltonian for which a certain non-resonance condition holds.read more
Citations
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Multidimensional continued fractions, dynamical renormalization and KAM theory
TL;DR: In this article, the authors describe a simple algorithm based on the dynamics of flows on the homogeneous space of lattices of covolume one for the linearization of vector fields on tori of arbitrary dimension.
Journal ArticleDOI
Renormalizations and Rigidity Theory for Circle Homeomorphisms with Singularities of the Break Type
Konstantin Khanin,D. Khmelev +1 more
TL;DR: In this article, it was shown that any two homeomorphisms with a single break point are smoothly conjugate to each other provided they have the same quadratic irrational rotation number and the same size of a break.
Journal ArticleDOI
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
TL;DR: In this article, the authors studied the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods, and showed that the break-up of invariant tori is a universal mechanism.
Journal ArticleDOI
On the renormalization of Hamiltonian flows, and critical invariant tori
TL;DR: In this article, the authors analyzed a renormalization group transformation for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable fixed points.
Journal ArticleDOI
Renormalization and destruction of 1/γ2 tori in the standard nontwist map
TL;DR: In this paper, the authors extended the work of del-Castillo-Negrete, Greene, and Morrison on the standard nontwist map and studied the breakup of an invariant torus with winding number equal to the inverse golden mean squared.
References
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TL;DR: In this article, the Calculus of itineraries is used to describe the properties of one-parameter families of maps and the relative frequency of periodic and aperiodic behavior.
Journal ArticleDOI
A method for determining a stochastic transition
TL;DR: In this article, the existence of a KAM surface is assumed to be associated with a sudden change from stability to instability of nearby periodic orbits, which is consistent with all that is known, strongly supported by numerical results.
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TL;DR: In this paper, the universal one parameter family discussion renormalization for maps on a circle has been discussed, as well as period doubling in area-preserving maps: period doubling sequencers.
Journal ArticleDOI
Renormalization method for computing the threshold of the large-scale stochastic instability in two degrees of freedom Hamiltonian systems
Dominique Escande,F. Doveil +1 more
TL;DR: In this paper, an approximate renormalization procedure is derived for the HamiltonianH(v,x,t)=v2/2−M cosx−P cosk(x−t).
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