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Billiards With Positive Topological Entropy
, 2001
"... We prove that billiard flows on strictly convex tables with a sufficiently small circular scatterer generically admit positive topological entropy. In particular we show that billiard systems in nonconcentric circular annuli have the same property for sufficiently small inner radii in both eucli ..."
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Cited by 3 (0 self)
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We prove that billiard flows on strictly convex tables with a sufficiently small circular scatterer generically admit positive topological entropy. In particular we show that billiard systems in nonconcentric circular annuli have the same property for sufficiently small inner radii in both
POSITIVE TOPOLOGICAL ENTROPY AND ℓ1
, 2003
"... Abstract. We characterize positive topological entropy for quasistate space homeomorphisms induced from C ∗algebra automorphisms in terms of dynamically generated subspaces isomorphic to ℓ1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particul ..."
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Cited by 2 (2 self)
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Abstract. We characterize positive topological entropy for quasistate space homeomorphisms induced from C ∗algebra automorphisms in terms of dynamically generated subspaces isomorphic to ℓ1. This geometric condition is also used to give a description of the topological Pinsker algebra
A Geometric Criterion For Positive Topological Entropy
 Comm. Math. Phys
, 1997
"... . We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement for heteroclinic points. We apply these results to study areapreserving perturbations of areapreserv ..."
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Cited by 28 (1 self)
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. We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement for heteroclinic points. We apply these results to study areapreserving perturbations of area
Special automorphisms of rational surfaces with positive topological entropy
 INDIANA UNIV. MATH. J
"... A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite mysterious and have been recently the object of intensive st ..."
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Cited by 8 (6 self)
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A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite mysterious and have been recently the object of intensive
Genericity Of Geodesic Flows With Positive Topological Entropy On S²
 J. DIFFERENTIAL GEOM.
, 2002
"... We show that the set of C # riemannian metrics on S² or RP² whose geodesic flow has positive topological entropy is open and dense in the C² topology. The proof is partially based on an analogue of Franks' lemma for geodesic flows on surfaces. ..."
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Cited by 20 (4 self)
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We show that the set of C # riemannian metrics on S² or RP² whose geodesic flow has positive topological entropy is open and dense in the C² topology. The proof is partially based on an analogue of Franks' lemma for geodesic flows on surfaces.
POSITIVE TOPOLOGICAL ENTROPY FOR MAGNETIC FLOWS ON SURFACES.
, 2006
"... Abstract. We study the topological entropy of the magnetic flow on closed riemannian surface. We prove that if the magnetic flow has a nonhyperbolic closed orbit in some energy set T c M = E −1 (c), then there exists an exact C ∞perturbation of the 2form Ω such that the new magnetic flow has posi ..."
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positive topological entropy in T c M. We also prove that if the magnetic flow has an infinite number of closed orbits in T c M, then there exists an exact C 1perturbation of Ω with positive topological entropy in T c M. The proof of the last result is based on an analogue of Frank’s lemma for magnetic
C ∞ genericity of positive topological entropy for geodesic flows
 on S 2 . J. Differential Geom
"... We show that there is a C ∞ open and dense set of positively curved metrics on S 2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for each of these metrics possesses a horseshoe and it follows that these metrics have an exponential growth ..."
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Cited by 2 (0 self)
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We show that there is a C ∞ open and dense set of positively curved metrics on S 2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for each of these metrics possesses a horseshoe and it follows that these metrics have an exponential growth
A remark on positive topological entropy of Nbuffer switched flow networks,”
 Discrete Dynamics in Nature and Society,
, 2005
"... We present a simpler elementary proof on positive topological entropy of the Nbuffer switched flow networks based on a new simple theorem on positive topological entropy of continuous map on compact metric space. ..."
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Cited by 1 (0 self)
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We present a simpler elementary proof on positive topological entropy of the Nbuffer switched flow networks based on a new simple theorem on positive topological entropy of continuous map on compact metric space.
Positive topological entropy for multibump magnetic fields Positive topological entropy for multibump magnetic fields
"... Abstract We study the dynamics of a charged particle in a planar magnetic field which consists of n ≥ 1 disjoint localized peaks. We show that, under mild geometric conditions, this system is semiconjugated to the full shift on n symbols and, hence, carries positive topological entropy. ..."
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Abstract We study the dynamics of a charged particle in a planar magnetic field which consists of n ≥ 1 disjoint localized peaks. We show that, under mild geometric conditions, this system is semiconjugated to the full shift on n symbols and, hence, carries positive topological entropy.
Results 1  10
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7,228