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Author ID: vivaldi.franco Recent zbMATH articles by "Vivaldi, Franco"
Published as: Vivaldi, Franco; Vivaldi, F.; Vivaldi, F. M.
Homepage: http://www.maths.qmul.ac.uk/~fvivaldi/
External Links: MGP
Documents Indexed: 61 Publications since 1981, including 2 Books
1 Contribution as Editor · 1 Further Contribution
Reviewing Activity: 128 Reviews
Co-Authors: 42 Co-Authors with 53 Joint Publications
919 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

50 Publications have been cited 446 times in 277 Documents Cited by Year
Universal behaviour in families of area-preserving maps. Zbl 1194.37011
Greene, J. M.; Mackay, R. S.; Vivaldi, F.; Feigenbaum, M. J.
33
1981
Geometry of \(p\)-adic Siegel discs. Zbl 0822.11081
Arrowsmith, David K.; Vivaldi, Franco
27
1994
Arithmetical properties of strongly chaotic motions. Zbl 0616.58039
Percival, Ian; Vivaldi, Franco
26
1987
Quadratic rational rotations of the torus and dual lattice maps. Zbl 1012.37025
Kouptsov, K. L.; Lowenstein, J. H.; Vivaldi, F.
21
2002
Recursive tiling and geometry of piecewise rotations by \(\pi/7\). Zbl 1059.37031
Lowenstein, J. H.; Kouptsov, K. L.; Vivaldi, F.
21
2004
Quasi-periodicity, global stability and scaling in a model of Hamiltonian round-off. Zbl 0933.37059
Lowenstein, John; Hatjispyros, Spyros; Vivaldi, Franco
20
1997
An algebraic geometric approach to integrable maps of the plane. Zbl 1117.14032
Jogia, Danesh; Roberts, John A. G.; Vivaldi, Franco
18
2006
Global stability of a class of discontinuous dual billiards. Zbl 0653.58018
Vivaldi, Franco; Shaidenko, Anna V.
18
1987
Bifurcations and discriminants for polynomial maps. Zbl 0827.12001
Morton, Patrick; Vivaldi, Franco
15
1995
Numerical study of billiard motion in an annulus bounded by non-concentric circles. Zbl 1194.65125
Saitô, N.; Hirooka, H.; Ford, J.; Vivaldi, F.; Walker, G. H.
14
1982
Embedding dynamics for round-off errors near a periodic orbit. Zbl 0969.37038
Lowenstein, J. H.; Vivaldi, F.
13
2000
Anomalous transport in a model of Hamiltonian round-off. Zbl 0917.58035
Lowenstein, J. H.; Vivaldi, F.
12
1998
Dynamics over irreducible polynomials. Zbl 0762.58020
Vivaldi, Franco
12
1992
A theory of modulational diffusion. Zbl 0584.58033
Chirikov, B. V.; Lieberman, M. A.; Shepel’yanskij, D. L.; Vivaldi, F. M.
11
1985
Galois theory of periodic orbits of rational maps. Zbl 0767.11049
Vivaldi, Franco; Hatjispyros, Spyros
11
1992
Mode-locking in coupled map lattices. Zbl 1194.37048
Carretero-González, R.; Arrowsmith, D. K.; Vivaldi, F.
10
1997
Arithmetical method to detect integrability in maps. Zbl 1267.37058
Roberts, J. A. G.; Vivaldi, F.
10
2003
Sticky orbits in a kicked-oscillator model. Zbl 1098.37066
Lowenstein, J. H.; Poggiaspalla, G.; Vivaldi, F.
9
2005
Round-off errors and \(p\)-adic numbers. Zbl 1009.65077
Bosio, D.; Vivaldi, F.
8
2000
Periodicity and transport from round-off errors. Zbl 0832.58017
Vivaldi, Franco
8
1994
Pseudo-randomness of round-off errors in discretized linear maps on the plane. Zbl 1057.37044
Vivaldi, Franco; Vladimirov, Igor
8
2003
A linear code for the sawtooth and cat maps. Zbl 0647.58031
Percival, Ian; Vivaldi, Franco
8
1987
Periodic orbits of the sawtooth maps. Zbl 0648.58027
Bird, Nigel; Vivaldi, Franco
8
1988
An algorithmic view of pseudochaos. Zbl 0960.81022
Chirikov, B. V.; Vivaldi, F.
7
1999
Critical function and modular smoothing. Zbl 0734.58030
Buric, N.; Percival, I. C.; Vivaldi, F.
7
1990
Analytically solvable dynamical systems which are not integrable. Zbl 0597.58009
Eckhardt, Bruno; Ford, Joseph; Vivaldi, Franco
7
1984
The arithmetic of discretized rotations. Zbl 1152.37329
Vivaldi, Franco
7
2006
Interval exchange transformations over algebraic number fields: the cubic Arnoux-Yoccoz model. Zbl 1128.37026
Lowenstein, J. H.; Poggiaspalla, G.; Vivaldi, F.
7
2007
Signature of time-reversal symmetry in polynomial automorphisms over finite fields. Zbl 1084.37035
Roberts, John A. G.; Vivaldi, Franco
6
2005
Geometric representation of interval exchange maps over algebraic number fields. Zbl 1141.37020
Poggiaspalla, G.; Lowenstein, J. H.; Vivaldi, F.
6
2008
Ideal orbits of toral automorphisms. Zbl 0694.58033
Bartuccelli, Michele; Vivaldi, Franco
5
1989
A combinatorial model for reversible rational maps over finite fields. Zbl 1171.37321
Roberts, John A. G.; Vivaldi, Franco
5
2009
Geometry of linear maps over finite fields. Zbl 0755.58031
Vivaldi, Franco
5
1992
Arithmetical theory of Anosov diffeomorphisms. Zbl 0643.58016
Vivaldi, F.
5
1987
Renormalization of one-parameter families of piecewise isometries. Zbl 1418.37074
Lowenstein, J. H.; Vivaldi, F.
5
2016
Critical dynamics and trees. Zbl 0662.58038
Percival, Ian; Vivaldi, Franco
4
1988
Complexity of regular invertible \(p\)-adic motions. Zbl 1080.37564
Pettigrew, J.; Roberts, J. A. G.; Vivaldi, F.
3
2001
Arithmetical properties of a family of irrational piecewise rotations. Zbl 1100.37028
Vivaldi, F.; Lowenstein, J. H.
3
2006
Algebraic number theory and Hamiltonian chaos. Zbl 0706.58039
Vivaldi, F.
3
1990
Approach to a rational rotation number in a piecewise isometric system. Zbl 1218.37049
Lowenstein, J. H.; Vivaldi, F.
3
2010
Near-integrable behaviour in a family of discretized rotations. Zbl 1273.37035
Reeve-Black, Heather; Vivaldi, Franco
3
2013
Geometrical properties of the mean-median map. Zbl 1448.37024
Hoseana, Jonathan; Vivaldi, Franco
2
2020
Small perturbations of a discrete twist map. Zbl 0932.37025
Zhang, Xu-Sheng; Vivaldi, Franco
2
1998
Some statistical properties of discretized quasiperiodic orbits. Zbl 0908.58050
Nucinkis, D.; Arrowsmith, D. K.; Vivaldi, F.
2
1997
Distribution of periodic orbits for the Casati-Prosen map on rational lattices. Zbl 1338.37055
Neumärker, Natascha; Roberts, John A. G.; Vivaldi, Franco
2
2012
A family of rational zeta functions for the quadratic map. Zbl 0827.58046
Hatjispyros, Spyros; Vivaldi, Franco
2
1995
Cauchy distributions for the integrable standard map. Zbl 1448.37077
Bountis, Anastasios; Veerman, J. J. P.; Vivaldi, Franco
1
2020
Cellular automata and finite fields. Zbl 0891.11061
Vivaldi, Franco
1
1994
Asymptotics in a family of linked strip maps. Zbl 1364.37097
Reeve-Black, Heather; Vivaldi, Franco
1
2015
Arithmetic exponents in piecewise-affine planar maps. Zbl 1364.37182
Roberts, John A. G.; Vivaldi, Franco
1
2015
Geometrical properties of the mean-median map. Zbl 1448.37024
Hoseana, Jonathan; Vivaldi, Franco
2
2020
Cauchy distributions for the integrable standard map. Zbl 1448.37077
Bountis, Anastasios; Veerman, J. J. P.; Vivaldi, Franco
1
2020
Renormalization of one-parameter families of piecewise isometries. Zbl 1418.37074
Lowenstein, J. H.; Vivaldi, F.
5
2016
Asymptotics in a family of linked strip maps. Zbl 1364.37097
Reeve-Black, Heather; Vivaldi, Franco
1
2015
Arithmetic exponents in piecewise-affine planar maps. Zbl 1364.37182
Roberts, John A. G.; Vivaldi, Franco
1
2015
Near-integrable behaviour in a family of discretized rotations. Zbl 1273.37035
Reeve-Black, Heather; Vivaldi, Franco
3
2013
Distribution of periodic orbits for the Casati-Prosen map on rational lattices. Zbl 1338.37055
Neumärker, Natascha; Roberts, John A. G.; Vivaldi, Franco
2
2012
Approach to a rational rotation number in a piecewise isometric system. Zbl 1218.37049
Lowenstein, J. H.; Vivaldi, F.
3
2010
A combinatorial model for reversible rational maps over finite fields. Zbl 1171.37321
Roberts, John A. G.; Vivaldi, Franco
5
2009
Geometric representation of interval exchange maps over algebraic number fields. Zbl 1141.37020
Poggiaspalla, G.; Lowenstein, J. H.; Vivaldi, F.
6
2008
Interval exchange transformations over algebraic number fields: the cubic Arnoux-Yoccoz model. Zbl 1128.37026
Lowenstein, J. H.; Poggiaspalla, G.; Vivaldi, F.
7
2007
An algebraic geometric approach to integrable maps of the plane. Zbl 1117.14032
Jogia, Danesh; Roberts, John A. G.; Vivaldi, Franco
18
2006
The arithmetic of discretized rotations. Zbl 1152.37329
Vivaldi, Franco
7
2006
Arithmetical properties of a family of irrational piecewise rotations. Zbl 1100.37028
Vivaldi, F.; Lowenstein, J. H.
3
2006
Sticky orbits in a kicked-oscillator model. Zbl 1098.37066
Lowenstein, J. H.; Poggiaspalla, G.; Vivaldi, F.
9
2005
Signature of time-reversal symmetry in polynomial automorphisms over finite fields. Zbl 1084.37035
Roberts, John A. G.; Vivaldi, Franco
6
2005
Recursive tiling and geometry of piecewise rotations by \(\pi/7\). Zbl 1059.37031
Lowenstein, J. H.; Kouptsov, K. L.; Vivaldi, F.
21
2004
Arithmetical method to detect integrability in maps. Zbl 1267.37058
Roberts, J. A. G.; Vivaldi, F.
10
2003
Pseudo-randomness of round-off errors in discretized linear maps on the plane. Zbl 1057.37044
Vivaldi, Franco; Vladimirov, Igor
8
2003
Quadratic rational rotations of the torus and dual lattice maps. Zbl 1012.37025
Kouptsov, K. L.; Lowenstein, J. H.; Vivaldi, F.
21
2002
Complexity of regular invertible \(p\)-adic motions. Zbl 1080.37564
Pettigrew, J.; Roberts, J. A. G.; Vivaldi, F.
3
2001
Embedding dynamics for round-off errors near a periodic orbit. Zbl 0969.37038
Lowenstein, J. H.; Vivaldi, F.
13
2000
Round-off errors and \(p\)-adic numbers. Zbl 1009.65077
Bosio, D.; Vivaldi, F.
8
2000
An algorithmic view of pseudochaos. Zbl 0960.81022
Chirikov, B. V.; Vivaldi, F.
7
1999
Anomalous transport in a model of Hamiltonian round-off. Zbl 0917.58035
Lowenstein, J. H.; Vivaldi, F.
12
1998
Small perturbations of a discrete twist map. Zbl 0932.37025
Zhang, Xu-Sheng; Vivaldi, Franco
2
1998
Quasi-periodicity, global stability and scaling in a model of Hamiltonian round-off. Zbl 0933.37059
Lowenstein, John; Hatjispyros, Spyros; Vivaldi, Franco
20
1997
Mode-locking in coupled map lattices. Zbl 1194.37048
Carretero-González, R.; Arrowsmith, D. K.; Vivaldi, F.
10
1997
Some statistical properties of discretized quasiperiodic orbits. Zbl 0908.58050
Nucinkis, D.; Arrowsmith, D. K.; Vivaldi, F.
2
1997
Bifurcations and discriminants for polynomial maps. Zbl 0827.12001
Morton, Patrick; Vivaldi, Franco
15
1995
A family of rational zeta functions for the quadratic map. Zbl 0827.58046
Hatjispyros, Spyros; Vivaldi, Franco
2
1995
Geometry of \(p\)-adic Siegel discs. Zbl 0822.11081
Arrowsmith, David K.; Vivaldi, Franco
27
1994
Periodicity and transport from round-off errors. Zbl 0832.58017
Vivaldi, Franco
8
1994
Cellular automata and finite fields. Zbl 0891.11061
Vivaldi, Franco
1
1994
Dynamics over irreducible polynomials. Zbl 0762.58020
Vivaldi, Franco
12
1992
Galois theory of periodic orbits of rational maps. Zbl 0767.11049
Vivaldi, Franco; Hatjispyros, Spyros
11
1992
Geometry of linear maps over finite fields. Zbl 0755.58031
Vivaldi, Franco
5
1992
Critical function and modular smoothing. Zbl 0734.58030
Buric, N.; Percival, I. C.; Vivaldi, F.
7
1990
Algebraic number theory and Hamiltonian chaos. Zbl 0706.58039
Vivaldi, F.
3
1990
Ideal orbits of toral automorphisms. Zbl 0694.58033
Bartuccelli, Michele; Vivaldi, Franco
5
1989
Periodic orbits of the sawtooth maps. Zbl 0648.58027
Bird, Nigel; Vivaldi, Franco
8
1988
Critical dynamics and trees. Zbl 0662.58038
Percival, Ian; Vivaldi, Franco
4
1988
Arithmetical properties of strongly chaotic motions. Zbl 0616.58039
Percival, Ian; Vivaldi, Franco
26
1987
Global stability of a class of discontinuous dual billiards. Zbl 0653.58018
Vivaldi, Franco; Shaidenko, Anna V.
18
1987
A linear code for the sawtooth and cat maps. Zbl 0647.58031
Percival, Ian; Vivaldi, Franco
8
1987
Arithmetical theory of Anosov diffeomorphisms. Zbl 0643.58016
Vivaldi, F.
5
1987
A theory of modulational diffusion. Zbl 0584.58033
Chirikov, B. V.; Lieberman, M. A.; Shepel’yanskij, D. L.; Vivaldi, F. M.
11
1985
Analytically solvable dynamical systems which are not integrable. Zbl 0597.58009
Eckhardt, Bruno; Ford, Joseph; Vivaldi, Franco
7
1984
Numerical study of billiard motion in an annulus bounded by non-concentric circles. Zbl 1194.65125
Saitô, N.; Hirooka, H.; Ford, J.; Vivaldi, F.; Walker, G. H.
14
1982
Universal behaviour in families of area-preserving maps. Zbl 1194.37011
Greene, J. M.; Mackay, R. S.; Vivaldi, F.; Feigenbaum, M. J.
33
1981
all top 5

Cited by 388 Authors

27 Vivaldi, Franco
10 Lowenstein, John H.
8 Mañosa, Víctor
7 Doyle, John R.
7 Roberts, John Anthony Gerard
6 Khrennikov, Andreĭ Yur’evich
6 Meiss, James D.
5 Bastien, Guy
5 Cima, Anna
5 Fu, Xinchu
5 Rogalski, Marc
5 Vaienti, Sandro
4 Gasull, Armengol
4 Goetz, Arek
4 Kahng, Byungik
4 Korhonen, Risto
4 Lindahl, Karl-Olof
4 Morton, Patrick
4 Mukhamedov, Farruh Maksutovich
4 Tabachnikov, Serge L.
4 Zaslavskiĭ, Georgiĭ Moiseevich
3 Ashwin, Peter
3 Beck, Christian
3 Dettmann, Carl P.
3 Efthymiopoulos, Christos
3 Fernandez, Bastien
3 Gallavotti, Giovanni M.
3 Gentile, Guido
3 Mañosas, Francesc
3 Oliveira, Diego F. M.
3 Percival, Ian C.
3 Poggiaspalla, Guillaume
3 Porter, Mason Alexander
3 Quispel, Gilles Reinout Willem
3 Saito, Asaki
3 Silverman, Joseph Hillel
3 Tanikawa, Kiyotaka
3 Yurova, Ekaterina I.
2 Akiyama, Shigeki
2 Anashin, Vladimir Sergeevich
2 Arrowsmith, David K.
2 Bruin, Henk
2 Capel, Hans W.
2 Carretero-González, Ricardo
2 Chen, Fei
2 Cincotta, Pablo M.
2 Cobo, Milton
2 Coutinho, Ricardo
2 de la Llave, Rafael
2 Degli Esposti, Mirko
2 Ezra, Gregory S.
2 Gaivão, José Pedro
2 Groote, Stefan
2 Gutiérrez-Romo, Rodolfo
2 Gutkin, Eugene
2 Halburd, Rodney G.
2 Hooper, W. Patrick
2 Kocarev, Ljupco
2 Kuznetsov, Sergey P.
2 Liao, Xiaofeng
2 Llibre, Jaume
2 Neumärker, Natascha
2 Páez, Rocío Isabel
2 Peres, Pedro L. D.
2 Pethő, Attila
2 Quas, Anthony
2 Rodrigues, Ana
2 Sataev, Igor’ Rustamovich
2 Schmidt, Thomas A.
2 Shparlinski, Igor E.
2 Shui, Shuliang
2 Siboni, Stefano
2 Stevens, John G.
2 Surer, Paul
2 Thomas, Diana Maria
2 Tsuchiya, Masa
2 Turchetti, Giorgio
2 van der Kamp, Peter H.
2 Wong, Kwokwo
2 Yamaguchi, Akihiro
2 Yamaguchi, Yoshihiro
2 Yi, Ren
2 Yu, Rongzhong
2 Zhang, Hongkun
1 Abarenkova, Nina
1 Adler, Roy Lee
1 Afraimovich, Valentin S.
1 Ahnert, Karsten
1 Aihara, Kazuyuki
1 Alevy, Ian
1 Altmann, Eduardo G.
1 Alwani, Fairuz
1 Amar, V.
1 Amigó, José María
1 Anglès d’Auriac, Jean-Christian
1 Arnol’d, Vladimir Igorevich
1 Arnoux, Pierre
1 Aston, Philip J.
1 Axelsson, E. I. Yurova
1 Axelsson, E. Yurova
...and 288 more Authors
all top 5

Cited in 99 Serials

38 Chaos
30 Physica D
16 Dynamical Systems
10 Journal of Statistical Physics
10 Ergodic Theory and Dynamical Systems
9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 Journal of Mathematical Physics
7 Communications in Mathematical Physics
7 Transactions of the American Mathematical Society
6 Experimental Mathematics
6 Communications in Nonlinear Science and Numerical Simulation
6 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
5 Chaos, Solitons and Fractals
4 Celestial Mechanics and Dynamical Astronomy
3 Physica A
3 Advances in Mathematics
3 Journal of Difference Equations and Applications
2 International Journal of Theoretical Physics
2 Israel Journal of Mathematics
2 Journal of Mathematical Analysis and Applications
2 Nonlinearity
2 Physics Letters. A
2 Rocky Mountain Journal of Mathematics
2 Geometriae Dedicata
2 Mathematische Zeitschrift
2 Topology and its Applications
2 Bulletin of the American Mathematical Society. New Series
2 Annales de l’Institut Henri Poincaré. Physique Théorique
2 Finite Fields and their Applications
2 Conformal Geometry and Dynamics
2 Qualitative Theory of Dynamical Systems
2 Journal of Nonlinear Mathematical Physics
2 Proceedings of the Steklov Institute of Mathematics
2 Journal of Modern Dynamics
2 Journal of Computational Dynamics
1 International Journal of Modern Physics B
1 Bulletin of the Australian Mathematical Society
1 Computers & Mathematics with Applications
1 Computer Physics Communications
1 Journal of Fluid Mechanics
1 Linear and Multilinear Algebra
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Nuclear Physics. B
1 Reviews of Modern Physics
1 Wave Motion
1 The Mathematical Intelligencer
1 Acta Arithmetica
1 Annales de l’Institut Fourier
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 Compositio Mathematica
1 Duke Mathematical Journal
1 Inventiones Mathematicae
1 Journal of Algebra
1 Journal of Differential Equations
1 Journal of the Korean Mathematical Society
1 Journal of Number Theory
1 Proceedings of the American Mathematical Society
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Proceedings of the London Mathematical Society. Third Series
1 Theoretical Computer Science
1 Theoretical Population Biology
1 Transactions of the Moscow Mathematical Society
1 Circuits, Systems, and Signal Processing
1 Applied Numerical Mathematics
1 Boletim da Sociedade Portuguesa de Matemática
1 Journal of the American Mathematical Society
1 Computational Mathematics and Mathematical Physics
1 Automation and Remote Control
1 Elemente der Mathematik
1 Linear Algebra and its Applications
1 Indagationes Mathematicae. New Series
1 Calculus of Variations and Partial Differential Equations
1 Journal de Théorie des Nombres de Bordeaux
1 Physics of Fluids
1 The New York Journal of Mathematics
1 Selecta Mathematica. New Series
1 Electronic Research Announcements of the American Mathematical Society
1 Izvestiya: Mathematics
1 Discrete and Continuous Dynamical Systems
1 Nonlinear Dynamics
1 Mathematical Physics, Analysis and Geometry
1 Regular and Chaotic Dynamics
1 Journal of the European Mathematical Society (JEMS)
1 International Journal of Modern Physics C
1 Physical Review Letters
1 Advances in Geometry
1 Physical Review E. Third Series
1 Computational Methods and Function Theory
1 SIAM Journal on Applied Dynamical Systems
1 International Journal of Geometric Methods in Modern Physics
1 Sarajevo Journal of Mathematics
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 Mathematics in Computer Science
1 Algebra & Number Theory
1 Research in the Mathematical Sciences
1 Arnold Mathematical Journal
1 Research in Number Theory
1 Journal of Siberian Federal University. Mathematics & Physics
1 Actes des Rencontres du C.I.R.M.
all top 5

Cited in 39 Fields

233 Dynamical systems and ergodic theory (37-XX)
49 Number theory (11-XX)
25 Mechanics of particles and systems (70-XX)
21 Statistical mechanics, structure of matter (82-XX)
20 Difference and functional equations (39-XX)
15 Algebraic geometry (14-XX)
14 Quantum theory (81-XX)
10 Field theory and polynomials (12-XX)
10 Numerical analysis (65-XX)
9 Ordinary differential equations (34-XX)
9 Information and communication theory, circuits (94-XX)
7 Partial differential equations (35-XX)
7 Convex and discrete geometry (52-XX)
6 Measure and integration (28-XX)
6 Computer science (68-XX)
5 Combinatorics (05-XX)
5 Group theory and generalizations (20-XX)
5 Functions of a complex variable (30-XX)
5 Probability theory and stochastic processes (60-XX)
4 Several complex variables and analytic spaces (32-XX)
4 Fluid mechanics (76-XX)
3 Real functions (26-XX)
3 Functional analysis (46-XX)
3 Differential geometry (53-XX)
3 General topology (54-XX)
3 Manifolds and cell complexes (57-XX)
3 Global analysis, analysis on manifolds (58-XX)
2 General and overarching topics; collections (00-XX)
2 Mathematical logic and foundations (03-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Special functions (33-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Operator theory (47-XX)
2 Biology and other natural sciences (92-XX)
2 Systems theory; control (93-XX)
1 Commutative algebra (13-XX)
1 Topological groups, Lie groups (22-XX)
1 Geometry (51-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year