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All Periodic Orbits With Period
"... In this paper we discuss the possibility of using interval Newton method for identification of periodic orbits in discretetime 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 discretetime 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
"... 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
 TRANS. AMER. MATH. SOC
, 1989
"... We introduce some notions that are useful for studying the behavior of periodic orbits of maps of onedimensional 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 ..."
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Cited by 9 (0 self)
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We introduce some notions that are useful for studying the behavior of periodic orbits of maps of onedimensional 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
, 2006
"... It is shown that the set of 4period 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. ..."
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Cited by 4 (1 self)
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It is shown that the set of 4period 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
, 2009
"... Let f: M → M be a C 1+εmap on a smooth Riemannian manifold M and let Λ ⊂ M be a compact finvariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of fΛ. These results are noninvertible and, in particular, nonuniformly hyperbolic ..."
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Cited by 3 (0 self)
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Let f: M → M be a C 1+εmap on a smooth Riemannian manifold M and let Λ ⊂ M be a compact finvariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of fΛ. These results are noninvertible and, in particular, nonuniformly hyperbolic
Periodic Orbits in Polygonal Billiards ∗
, 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
, 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
, 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
, 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
 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 ..."
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Cited by 9 (5 self)
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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
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7,388