Dold sequences, periodic points, and dynamics

DOI10.1112/blms.12531zbMath1504.11038arXiv2007.04031OpenAlexW3041162019MaRDI QIDQ5021644

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Publication date: 13 January 2022

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.04031

zbMATH Keywords

periodic pointsDold sequences

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Sequences (mod (m)) (11B50)

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Generalized Dold sequences on partially-ordered sets, On partially periodic point free self-maps on the wedge sums of spheres, Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere, Cycles, Eulerian digraphs and the Schönemann-Gauss theorem

Cites Work

• Linear recurrence sequences satisfying congruence conditions
• Orbit-counting in non-hyperbolic dynamical systems
• Twisted Burnside-Frobenius theory for discrete groups
• The matrix Euler-Fermat theorem
• Differentiable dynamical systems
• Some fixed point theorems
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Indices of iterations and periodic points of simplicial maps of smooth type.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fixed point indices of planar continuous maps
• Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
• 70 Years of asymptotic fixed point theory
• Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
• Minimizing the number of periodic points for smooth maps. Non-simply connected case
• Fixed point indices of iterated smooth maps in arbitrary dimension
• Generating sequences of Lefschetz numbers of iterates
• The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic orbits
• Congruences for sequences similar to Euler numbers
• Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms. I
• Dwork congruences and reflexive polytopes
• A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms
• On the matricial version of Fermat-Euler congruences
• On some number-theoretic conjectures of V. Arnold
• Extended Euler congruence
• Fixed point indices of iterated maps
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• The spectra of nonnegative matrices via symbolic dynamics
• A note on the set of periods for Klein bottle maps
• An index theorem for the homeomorphisms of the plane near a fixed point
• Finding periodic points of a map by use of a \(k\)-adic expansion
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• Some developments in Nielsen fixed point theory
• A \(q\)-microscope for supercongruences
• Dynamics on abelian varieties in positive characteristic
• Dynamics of field line mappings in magnetic flux tubes
• Generalized Fermat, double Fermat and Newton sequences.
• Fixed point indices of iterations of planar homeomorphisms
• An extension of the Artin-Mazur theorem
• Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms
• Generalized Dold sequences on partially-ordered sets
• The On-Line Encyclopedia of Integer Sequences
• Towards a Pólya-Carlson dichotomy for algebraic dynamics
• On periodic points
• Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes
• The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\)
• Ein Satz über den Leray-Schauderschen Abbildungsgrad. (Theorem on the Leray-Schauder degree of mappings)
• The zeta function of automorphisms of solenoid groups
• Traces of algebraic integers and dynamical systems
• Dwork’s congruences for the constant terms of powers of a Laurent polynomial
• The Nielsen and Reidemeister theories of iterations on infra-solvmanifolds of type (𝑅) and poly-Bieberbach groups
• Dynamical constraints from field line topology in magnetic flux tubes
• Indices of the iterates of ℝ³ -homeomorphisms at fixed points which are isolated invariant sets
• Orbits for products of maps
• Dynamically affine maps in positive characteristic
• Dirichlet series for finite combinatorial rank dynamics
• Periodic segment implies infinitely many periodic solutions
• MINIMAL SETS OF PERIODS FOR MAPS ON THE KLEIN BOTTLE
• Smoothness is not an obstruction to realizability
• The numbers of periodic orbits hidden at fixed points of n-dimensional holomorphic mappings
• Geometry of Reidemeister classes and twisted Burnside theorem
• A dichotomy in orbit growth for commuting automorphisms
• Orbit-counting for nilpotent group shifts
• Functorial orbit counting
• Realizability of integer sequences as differences of fixed point count sequences
• Lectures on Nielsen fixed point theory
• A Coloring Proof of a Generalisation of Fermat's Little Theorem
• The Nielsen Numbers of Homotopically Periodic Maps of Infranilmanifolds
• Periodic Orbits and Solenoids in Generic Hamiltonian Dynamical Systems
• Nielsen Numbers of Periodic Maps on Solvmanifolds
• On the Lefschetz Number for Iterates of Continuous Mappings
• On the Fixed Point Index of Iterates of Planar Homeomorphisms
• Almost all $S$-integer dynamical systems have many periodic points
• An Uncountable Family of Group Automorphisms, and a Typical Member
• On the use of the topological degree theory in broken orbits analysis
• The spectra of nonnegative integer matrices via formal power series
• Periodic points of holomorphic maps via Lefschetz numbers
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion
• Gauss congruences for rational functions in several variables
• Fermat's Little Theorem and Gauss Congruence: Matrix Versions and Cyclic Permutations
• Supercongruences for polynomial analogs of the Apéry numbers
• Dynamical properties of quasihyperbolic toral automorphisms
• Stirling numbers and periodic points
• Fibonacci along even powers is (almost) realizable
• On the Positivity Problem for Simple Linear Recurrence Sequences,
• Time-changes preserving zeta functions
• q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
• Dynamical zeta functions and Kummer congruences