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Homoclinic tangencies and dominated splittings
Nonlinearity, 2002Summary: We characterize diffeomorphisms that are \(C^1\) away from homoclinic tangencies by using dominated splittings on the \(C^1\) preperiodic sets. More precisely, we prove that a diffeomorphism \(f\) cannot be \(C^1\) approximated by systems with homoclinic tangencies if and only if for all \(1\leq i\leq d-1\), the \(C^1\) \(i\)-preperiodic set \(
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Adapted Metrics for Dominated splittings.
Ergodic Theory and Dynamical Systems, 2007A Riemannian metric is adapted to an hyperbolic set of a diffeomorphism if, for this metric, the expansion/contraction of the unstable/stable directions can be seen after only one iteration. A dominated splitting is a notion of weak hyperbolicity where the tangent bundle of the manifold splits in invariant subbundles such that the vector expansion on ...
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Neighborhood outer split domination in graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2019AbstractA neighborhood outer split dominating set (nosd-set) in a graph G is a dominating set S with the property that the sub graph induced by the open neighborhood of the set S is disconnected.
K. Suriya Prabha +3 more
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Integrability on codimension one dominated splitting
Bulletin of the Brazilian Mathematical Society, New Series, 2007We study the unique integrability of the center unstable subbundle of a codimension one dominated splitting.
Enrique R. Pujals*, Martin Sambarino
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Split domination of some special graph
AIP Conference Proceedings, 2022K. Suja, K. Vishwanathan
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Some Results on Accurate Split Domination And Accurate Non-Split Domination of Some Special Graphs
International Journal of Mathematics Trends and Technology, 2020Aswini T +2 more
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Split-Ring Structured All-Inorganic Perovskite Photodetector Arrays for Masterly Internet of Things
Nano-Micro Letters, 2022exaly
Single-cell profiling of the developing mouse brain and spinal cord with split-pool barcoding
Science, 2018Alexander B Rosenberg +2 more
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