Results 21 to 30 of about 166,810 (242)
Beyond the periodic orbit theory [PDF]
Nonlinearity, 1998 The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form.
Cvitanovic, P. +3 more
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On the distribution of periodic orbits
Discrete & Continuous Dynamical Systems - A, 2010 Let $f:M\to M$ be a $C^{1+ }$-map on a smooth Riemannian manifold $M$ and let $ \subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f| $. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by
Christian Wolf, Katrin Gelfert
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Periodic Orbit Theory of Diffraction [PDF]
Physical Review Letters, 1994 An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and which correspond to creping waves. A new family of resonances in the two disk scattering system can be well described
Vattay, G., Wirzba, A., Rosenqvist, P.
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Linear instability of periodic orbits of free period Lagrangian systems
Electronic Research Archive, 2022 Minimizing closed geodesics on surfaces are linearly unstable. By starting with this classical Poincaré's instability result, in the present paper we prove a result that allows to deduce the linear instability of periodic solutions of autonomous ...
Alessandro Portaluri, Li Wu , Ran Yang
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Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Abstract and Applied Analysis, 2012 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
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Global orbit of a complicated nonlinear system with the global dynamic frequency method
Journal of Low Frequency Noise, Vibration and Active Control, 2021 Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the ...
Zhixia Wang +3 more
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Measuring scars of periodic orbits [PDF]
Physical Review E, 1999 The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix theory. This paper discusses measures of scars and in so doing also tries to clarify the concepts and effects of ...
Lev Kaplan, Eric J. Heller
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On the periodic orbits of Hamiltonian systems [PDF]
Journal of Mathematical Physics, 2010 We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the ...
Llibre, Jaume, Rodrigues, Ana
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Abstract and Applied Analysis, 2013 This paper is mainly concerned with the existence, stability, and bifurcations of periodic solutions of a certain scalar impulsive differential equations on Moebius stripe.
Yefeng He, Yepeng Xing
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Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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