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A Topological Classification of Interval Map**s with Finitely Many Discontinuous Points
Topological conjugacy plays an important role in the study of dynamical systems and functional equations. In this paper, a topological classification...
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Homeomorphisms and Topological Invariants
In this chapter, we define those maps between two spaces which will make two spaces equivalent, hence indistinguishable from the topological point of...
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Topological Rigidity
In Section 19.2 we give a necessary and sufficient condition for topological rigidity in terms of the surgery exact sequence.
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On Topological Classification of Regular Denjoy Type Homeomorphisms
AbstractWe consider regular Denjoy type homeomorphisms of the two-dimensional torus which are the most natural generalization of Denjoy...
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Properties of Topological Partitions and Map**s of Topological Groups
In this paper, we examine topological partitions of topological spaces that arise in connection with continuous map**s of topological spaces. The...
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On Mathematical Aspects of the Theory of Topological Insulators
This review is devoted to one of the most interesting and actively develo** fields in condensed matter physics—theory of topological insulators....
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Topological Classification of Some SD Hamiltonian Systems
In this paper we classify the phase portraits in the Poincaré disk of the Smooth and Discontinuous (SD) Hamiltonian system with the rational...
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Topologically Semiperfect Topological Rings
We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show...
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On the Topological Classification of Structurally Stable Diffeomorphisms on 3-Manifolds with a 2-Dimensional Expanding Attractor
AbstractThe paper is devoted to the topological classification of structurally stable diffeomorphisms on three-dimensional manifolds whose...
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Topological mixing of positive diagonal flows
Let G be a connected, real linear, semisimple Lie group without compact factors and Γ < G a Zariski dense, discrete subgroup. We study the...
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Topological Conjugacy of Gradient-Like Flows on Surfaces and Efficient Algorithms for its Distinction
Gradient-like flows on surfaces have simple dynamics, which inspired many mathematicians to search for invariants of their topological equivalence....
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Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
In this chapter, we introduce and discuss the following fundamental notions that will be used throughout the book: topological equivalence of...
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On Embedding of the Morse–Smale Diffeomorphisms in a Topological Flow
This review presents the results of recent years on solving of the Palis problem on finding necessary and sufficient conditions for the embedding of...
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Topological mixing of random substitutions
We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is...
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Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space
Using operator algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space. Quantum...
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Brain chains as topological signatures for Alzheimer’s disease
Topology is providing new insights for neuroscience. For instance, graphs, simplicial complexes, directed graphs, flag complexes, persistent homology...
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GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back
Dubrovin establishes a certain relationship between the GUE partition function and the partition function of Gromov–Witten invariants of the complex...
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Quasi-Invariant and Invariant Functionals and Measures on Systems of Topological Loops and Quasigroups
Under study are the left-invariant, right-invariant, and quasi-invariant functionals and measures on topological loops and quasigroups. We also...
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Constructing Tree-Decompositions That Display All Topological Ends
We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.
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Cut-and-join operators in cohomological field theory and topological recursion
We construct a cubic cut-and-join operator description for the partition function of the Chekhov–Eynard–Orantin topological recursion for a local...