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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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Statistical properties of periodic orbits in 4-disk billiard system: pruning-proof property [PDF]
, 2005 Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic systems, pruning-
Alekseev +67 more
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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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The American Mathematical Monthly, 1920 Mode of access: Internet.
Moulton, Forest Ray, 1872-1952. +5 more
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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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Piecewise expanding maps: combinatorics, dynamics and representation of rational numbers
ESAIM: Proceedings and Surveys, 2014 We establish combinatorial properties of the dynamics of piecewise increasing, continuous, expanding maps of the interval such as description of periodic and pre-periodic points, primitiveness of truncated itineraries and length of ...
Serpa Cristina, Buescu Jorge
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Periodic-orbit theory of anderson localization on graphs [PDF]
Physical Review Letters, 1999 We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to
Schanz, Smilansky
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Periodic and homoclinic orbits in a toy climate model [PDF]
Nonlinear Processes in Geophysics, 1994 A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet.
M. Toner, A. D. Kirwan, Jr.
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