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All Periodic Orbits With Period

by For The Enon, Zbigniew Galias
"... In this paper we discuss the possibility of using interval Newton method for identification of periodic orbits in discrete--time dynamical systems. We describe the modification of this method called the global interval Newton method. We also introduce several improvements of this method. As an examp ..."
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In this paper we discuss the possibility of using interval Newton method for identification of periodic orbits in discrete--time dynamical systems. We describe the modification of this method called the global interval Newton method. We also introduce several improvements of this method

Finding Periodic Orbits With Generating

by Functions Guibout Scheeres, V. Guibout, D. J. Scheeres
"... Periodic orbits are studied using generating functions. We develop necessary and su#cient conditions for existence of periodic orbits of a given period or going through a given point in space. These conditions reduce the search to either solving a set of implicit equations, which can often be done g ..."
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Periodic orbits are studied using generating functions. We develop necessary and su#cient conditions for existence of periodic orbits of a given period or going through a given point in space. These conditions reduce the search to either solving a set of implicit equations, which can often be done

Periodic orbits of maps of Y

by Lluis Alsedà, Jaume Llibre, Michat Misiurewicz - TRANS. AMER. MATH. SOC , 1989
"... We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z e C: z3 e [0,1]} into itself having zero as a fixed point. We also obtain new pro ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z e C: z3 e [0,1]} into itself having zero as a fixed point. We also obtain new

Periodic Orbits in Outer Billiard

by Alexander Tumanov, Vadim Zharnitsky , 2006
"... It is shown that the set of 4-period orbits in outer billiard in the Euclidean plane with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a parallelogram. ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
It is shown that the set of 4-period orbits in outer billiard in the Euclidean plane with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a parallelogram.

ON THE DISTRIBUTION OF PERIODIC ORBITS

by Katrin Gelfert, Christian Wolf , 2009
"... Let f: M → M be a C 1+ε-map on a smooth Riemannian manifold M and let Λ ⊂ 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|Λ. These results are non-invertible and, in particular, non-uniformly hyperbolic ..."
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Let f: M → M be a C 1+ε-map on a smooth Riemannian manifold M and let Λ ⊂ 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|Λ. These results are non-invertible and, in particular, non-uniformly hyperbolic

Periodic Orbits in Polygonal Billiards ∗

by Debabrata Biswas , 1996
"... We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with t ..."
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We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation

TRANSFERS AND PERIODIC ORBITS OF HOMEOMORPHISMS

by Daniel Henry Gottlieb , 2008
"... Abstract. Bo Ju Jiang applied Neilsen theory to the study of periodic orbits of a homeomorphism. His method employs a certain loop in the mapping torus of the homeomorphism. Our interest concerns the persistence of periodic orbits in parameterized families of homeomorphisms. This leads us to conside ..."
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Abstract. Bo Ju Jiang applied Neilsen theory to the study of periodic orbits of a homeomorphism. His method employs a certain loop in the mapping torus of the homeomorphism. Our interest concerns the persistence of periodic orbits in parameterized families of homeomorphisms. This leads us

Beyond the Periodic Orbit Theory

by Predrag Cvitanovic, Kim Hansen, Juri Rolf, Gabor Vattay , 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 ..."
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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

Periodic Orbits in Arithmetical Chaos

by Jens Bolte , 1992
"... 1 Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the unconstrained motions of particles ..."
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1 Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the unconstrained motions

Reversible Relative Periodic Orbits

by Jeroen S.W. Lamb, Claudia Wulff - J. Dierential Equations , 1999
"... We study the bundle structure near reversible relative periodic orbits in reversible equivariant systems. In particular we show that the vector field on the bundle forms a skew product system, by which the study of bifurcation from reversible relative periodic solutions reduces to the analysis of bi ..."
Abstract - Cited by 9 (5 self) - Add to MetaCart
We study the bundle structure near reversible relative periodic orbits in reversible equivariant systems. In particular we show that the vector field on the bundle forms a skew product system, by which the study of bifurcation from reversible relative periodic solutions reduces to the analysis
Results 1 - 10 of 7,388